Keywords: Cyclic codes; Fibonacci numbers; Pell numbers; Quaternion algebras; 11B39; 11R54; 94B05; 94B15;
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Keywords: Fibonacci and Lucas sequences; Legendre symbol; 11A51; 11B39; 11B50;
Keywords: Bi-periodic Fibonacci matrix sequence; Bi-periodic Lucas matrix sequence; Bi-periodic Lucas number; Generalized Fibonacci matrix sequence; Generating function; 11B39; 15A24;
Keywords: primary; 11D61; secondary; 11B39; Exponential equation; Hemachandra numbers; Fibonacci numbers;
Keywords: Trinomial coefficient; Linear recurrence sequence; Chebyshev polynomial; Primary 11B65; Secondary 05A10; 05A19; 11B37; 11B39; 11A07;
Keywords: 11B39; 11A41; Generalized Fibonacci sequence; Fibonacci number; Lucas number; Pell sequence; Pell-Lucas sequence; Chebychev polynomial; Fibonacci polynomial; Lucas polynomial; Jacobsthal polynomial; Jacobsthal-Lucas polynomial; Lucas-Lehmer test;
Keywords: Generalized Tribonacci sequence; Third order recurrence; Counting; Generating function; Binet formula; Ising model; 11B39; 05A15; 75.10.Jm; 02.10.Ox;
Keywords: 15B05; 11B39; 11B65; Dual sequence; Dual matrix; Vandermonde matrix; Hankel matrix; Toeplitz matrix; Lagrange interpolation polynomial;
Keywords: 05A15; 05A05; 11B39; 11B73; 15B36; 15A06; 05A19; 11B83; Double Riordan arrays; Riordan group; Generating function; Succession rule; A-sequence; Z-sequence; High order Riordan arrays; Quasi-Riordan arrays;
Keywords: 11A63; 68R15; 11B39; Substitutions; Integer representation; Combinatorics on words;
Keywords: primary; 11B39; 11T55; Fibonacci polynomials; Lucas polynomials; Polynomial rings over finite fields;
Keywords: primary; 11A07; secondary; 11B39; 12Y05; Finite field; Order; Resultant; Primitive root; Primitive divisor;
Keywords: 15B18; 11B39; 11B65; Invariant sequence; Pascal matrix; Eigenvalue; Eigenvector;
Keywords: 05A15; 05A05; 11B39; 11B73; 15B36; 15A06; 05A19; 11B83Riordan arrays; Riordan group; Appell subgroup; Associate subgroup; Bell subgroup; Derivative subgroup; Checkerboard subgroup; Hitting-time subgroup; Girard–Waring type identities; Row sum functions an
Keywords: Cumulative growth; Fractional calculus; Rate equation; Mittag–Leffler26A33; 11B39; 33E12,
Keywords: 11B39; 11D45; 11D61; 11J25; 11J86Diophantine equations; Linear forms in logarithms; Generalized Fibonacci numbers; Reduction method
Keywords: primary; 11A15; secondary; 11A07; 11B39; 11E25; Reciprocity law; Octic residue; Congruence; Quartic Jacobi symbol; Lucas sequence;
Keywords: 11B39; 11J86Generalized Fibonacci numbers; Lower bounds for nonzero linear forms in logarithms of algebraic numbers
Keywords: 05A15; 05A05; 11B39; 11B73; 15B36; 15A06; 05A19; 11B83Riordan group; Generating function; Stieltjes matrix; Succession rule; Production matrix; A-matrix; Fundamental theorem of Riordan arrays; Stirling numbers of the second kind
Keywords: 11B37; 11B39; Integer sequences; Unique representations;
Keywords: 11B39; 12E20Linear recurrence relation; Finite field; Standard subgroup; Restricted period
Keywords: 11B39; 11D61; 11J86Multiplicatively independent integers; Binary recurrent sequences; Lower bounds for nonzero linear forms in logarithms of algebraic numbers
On simultaneous Pell equations x2 â (a2 â 1)y2 = 1 and y2 â pz2 = 1
Keywords: 11B39; 11D61; Linear form in logarithms; Diophantine approximation;
The moments of the logarithm of a G.C.D. related to Lucas sequences
Keywords: primary; 11B37; secondary; 11B39; Greatest common divisor; Lucas sequences; Moments;
A new condition equivalent to the Ankeny-Artin-Chowla conjecture
Keywords: primary; 11B39; secondary; 11R27; 11R11; 11B37; 11B68; Ankeny-Artin-Chowla conjecture; Fundamental unit; Lucas polynomial;
The eigenvalues of r-periodic tridiagonal matrices by factorization of some recursive sequences
Keywords: 65F15; 15A18; 11B39; Tridiagonal matrices; Eigenvalues; Characteristic polynomials; Conditional recurrences; Continued fractions; Continuants;
On a variant of Pillai's problem II
Keywords: 11D61; 11B39; 11D45; Diophantine equations; Pillai's problem; Recurrence sequence;
On the equation Vn=wx2â1
Keywords: 11B37; 11B39; 11B50; 11B99; 11D41; Lucas sequence of the second kind; Congruences; Diophantine equations;
Primefree shifted Lucas sequences of the second kind
Keywords: primary; 11B37; 11B39; secondary; 11B83; Lucas sequences; Primefree; Coverings;
The 2-adic valuation of generalized Fibonacci sequences with an application to certain Diophantine equations
Keywords: 11B39; 11B65; 11D99; Generalized Fibonacci sequences; Diophantine equations; Factorials; p-adic valuation;
Generalized Humbert polynomials via generalized Fibonacci polynomials
Keywords: Generalized (p, q)-Fibonacci polynomials; Generalized (p, q)-Lucas polynomials; Generalized Humbert polynomials; Combinatorial identities; Determinants; 05A15; 05A19; 11B39;
Partial differential equations for a new family of numbers and polynomials unifying the Apostol-type numbers and the Apostol-type polynomials
Keywords: primary; 05A10; 05A15; 11B37; 11B39; 11B68; 11B83; 11M35; 26C05; 26C10; secondary; 33C05; 34A99; 35A99; Generating functions; Functional equations; Partial differential equations; Hypergeometric functions; Hurwitz-Lerch zeta functions; Apostol-Bernoul
On a new generalization of Fibonacci quaternions
Keywords: Fibonacci sequence; Generalized Fibonacci sequence; Recurrence relations; Quaternions; 11B39; 05A15; 11R52;
On a conjecture of Ilmonen, Haukkanen and Merikoski concerning the smallest eigenvalues of certain GCD related matrices
Keywords: 15A18; 15A23; 15B36; 15B48; 11B39; 11C20; GCD matrix; (0,1)-matrix; Positive matrix; Eigenvalue; Spectral radius; Fibonacci number;
Nevanlinna extremal measures for polynomials related to q−1-Fibonacci polynomials
Keywords: 11B39; 33D45; 30E05q-Fibonacci polynomials; Orthogonal polynomials; Measure of orthogonality; N-extremal measures; q-exponential; q-sine; q-cosine
Double parameter recurrences for polynomials in bi-infinite Riordan matrices and some derived identities
Keywords: primary; 05A19; secondary; 11B39; 68R05; Combinatorial identities; Riordan matrix; Recurrences relations; Fibonacci sequence;
A note on h(x) â Fibonacci quaternion polynomials
Keywords: 11B39; 11R52; 05A15;
Carmichael numbers with p+1|n+1
Keywords: 11A51; 11Y11; 11B39; 11Y50; Baillie-PSW primality test; Carmichael number; Lucas-Carmichael number; Lucas primality test; Williams number; Pseudoprime;
Generalizations of a result of Christensen on renewal sequences and linear recurrences
Keywords: 60K05; 11B39; 39A10; Renewal sequences; Linear recurrences; Closed form solutions;
Congruences arising from Apéry-type series for zeta values
Keywords: 11B65; 05A10; 11B68; 11A07; 33F10; 11B39; 11M06; Congruence; Creative telescoping; WZ pair; Finite central binomial sum; Multiple harmonic sum; Bernoulli number; Apéry-like series; Zeta value;
LDU decomposition of an extension matrix of the Pascal matrix
Keywords: 11B39; 11B50Generalized Pascal matrix; Weighted lattice path; Lattice path matrix; LDU decomposition; Positive definite
Spanning forests and the golden ratio
Keywords: 05C50; 05C05; 05C12; 15A51; 11B39; 60J10Doubly stochastic graph matrix; Matrix forest theorem; Fibonacci numbers; Laplacian matrix; Vertex–vertex proximity; Spanning forest; Golden ratio
Fibonacci numbers, alternating parity sequences and faces of the tridiagonal Birkhoff polytope
Keywords: 05A15; 11B39; 52B11; 15A51Doubly stochastic matrix; Birkhoff polytope; Tridiagonal matrix; Number of vertices; Faces
Complete decomposition of Dickson-type polynomials and related Diophantine equations
Keywords: 30D05; 11B39; 11D45; 12E10; Polynomial decomposition; Dickson-type polynomials; Diophantine equations;
Logarithmic behavior of some combinatorial sequences
Keywords: 05A20; 05A16; 05E35; 11B83; 11B37; 11B39; 11B68Log-concavity; Log-convexity; Integer sequences; Catalan numbers; Motzkin numbers; Bell numbers; Secondary structures; Orthogonal polynomials
A factorization of the symmetric Pascal matrix involving the Fibonacci matrix
Keywords: 05A10; 11B39; 15A23Pascal matrix; Fibonacci matrix; Factorization of matrix
Bernoulli matrix and its algebraic properties
Keywords: 05A10; 05A19; 11B39; 11B68Bernoulli number; Bernoulli polynomial; Bernoulli Matrix; Generalized Pascal matrix; Fibonacci matrix
(±1)-Invariant sequences and truncated Fibonacci sequences
Keywords: 11B39; 11B50; Invariant sequence; Truncated Fibonacci sequence; Truncated Lucas sequence;
On a class of polynomials related to classical orthogonal and Fibonacci polynomials with probability applications
Keywords: 60C05; 62E15; 11B39; Orthogonal polynomials; Fibonacci polynomials; Convolution; Partial sum; Waiting time; Success runs; Probability mass function; Cumulative distribution function;
On the properties of Newton-Euler pairs
Keywords: 11B83; 15A15; 11B68; 05A17; 11A25; 11B73; 11B65; 11B39; Newton-Euler pair; Newton-Euler sequence; The sum of divisors; The number of partitions; Bernoulli numbers;