cp's OEIS Frontend

A334553 Number of Eulerian orientations in the n-Aztec diamond graph.

%I A334553 #8 Jun 07 2020 08:16:55
%S A334553 2,18,868,230274,338942604,2779683771636,127320422237993212,
%T A334553 32620173508191539578106,46794404527960763380238873820,
%U A334553 376118239460804805511929497668632684,16947204353591524393183053514633085861818452,4282329728316057313850583887700885027979305243679508
%N A334553 Number of Eulerian orientations in the n-Aztec diamond graph.
%C A334553 This sequence is based on the same Aztec diamond graph considered in A253107. In particular, it is the grid graph bounded by the eight equations x+y=-2n, x+y=2n, x-y=-2n, x-y=2n, x=1-2n, x=2n-1, y=1-2n, and y=2n-1.
%C A334553 An Eulerian orientation of a graph is an orientation of the edges such that every vertex has in-degree equal to out-degree.
%C A334553 All terms are even since reversing the orientation of every arc in any solution gives another solution.
%e A334553 a(2) = 18 because the edges of the graph illustrated below can be oriented in 18 different ways such that every vertex has in-degree equal to out-degree.
%e A334553           o---o
%e A334553           |   |
%e A334553       o---o---o---o
%e A334553       |   |   |   |
%e A334553       o---o---o---o
%e A334553           |   |
%e A334553           o---o
%Y A334553 Cf. A253107.
%K A334553 nonn
%O A334553 1,1
%A A334553 _Andrew Howroyd_, May 22 2020