A conjecture based on Somos-4 sequence and its extension

In two recent papers by Barry (2010) [29], and (2011) [30], it is conjectured that Somos-4 admits a solution expressed in terms of Hankel determinant with its elements satisfying a convolution recursion relation. In this paper, Barry’s conjecture on Somos-4 is firstly confirmed. Actually, we present a more generalized result. The proof is mainly based on new findings on properties for so-called Block–Hankel determinants. The method can also be used to prove another conjecture proposed by Michael Somos, which has been solved by Guoce Xin.