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%I #12 Nov 27 2022 11:32:16
%S 1,0,4,0,24,8,164,136,1236,1704,10116,19144,88616,205208,818764,
%T 2155160,7873440,22463400,77954740,233894600,788314984,2440865400,
%U 8095906076,25569342520,84107990356,269034666280
%N Number of n-step closed paths on the Cairo pentagonal lattice graph starting from a degree-4 node.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Cairo_pentagonal_tiling">Cairo pentagonal tiling</a>
%e For n=2, the a(2) = 4 solutions visit one of the four vertices adjacent to the initial vertex, and then return.
%e For n=5, the a(5) = 8 solutions consist of counterclockwise or clockwise traversals of the circumference of any of the four pentagons that surround the initial vertex.
%Y The accompanying sequences for the number of paths that return to a degree-3 node is A357811.
%Y Similar sequences for square, hexagonal, and honeycomb lattices are A002894, A002898 and A002893.
%K nonn,easy,walk
%O 0,3
%A _Dave R.M. Langers_, Oct 13 2022