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Number of n-step closed paths on the Cairo pentagonal lattice graph starting from a degree-3 node.
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%I #11 Nov 27 2022 11:32:27

%S 1,0,3,0,17,6,115,100,867,1236,7117,13770,62545,146866,579387,1537920,

%T 5581725,16002810,55329435,166465820,559913787,1736268432,5752600961,

%U 18182999274,59777071435,191287075320

%N Number of n-step closed paths on the Cairo pentagonal lattice graph starting from a degree-3 node.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Cairo_pentagonal_tiling">Cairo pentagonal tiling</a>

%e For n=2, the a(2) = 3 solutions visit one of the three vertices adjacent to the initial vertex, and then return.

%e For n=5, the a(5) = 6 solutions consist of counterclockwise or clockwise traversals of the circumference of any of the three pentagons that surround the initial vertex.

%Y The accompanying sequences for the number of paths that return to a degree-4 node is A357810.

%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