Proof of Blum's conjecture on hexagonal dungeons

Matt Blum conjectured that the number of tilings of the hexagonal dungeon of sides a, 2a, b, a, 2a, b   (where b⩾2ab⩾2a) is 132a214⌊a22⌋ (Propp, 1999 [4]). In this paper we present a proof for this conjecture using Kuo's Graphical Condensation Theorem (Kuo, 2004 [2]).