Proof of Blumʹs 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 ⩾ 2 a ) is 13 2 a 2 14 ⌊ a 2 2 ⌋ (Propp, 1999 [4]). In this paper we present a proof for this conjecture using Kuoʹs Graphical Condensation Theorem (Kuo, 2004 [2]).