A357811 - OEIS

A357811

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

1, 0, 3, 0, 17, 6, 115, 100, 867, 1236, 7117, 13770, 62545, 146866, 579387, 1537920, 5581725, 16002810, 55329435, 166465820, 559913787, 1736268432, 5752600961, 18182999274, 59777071435, 191287075320

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..25.

Wikipedia, Cairo pentagonal tiling

EXAMPLE

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

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.

CROSSREFS

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

Similar sequences for square, hexagonal, and honeycomb lattices are A002894, A002898 and A002893.

Sequence in context: A036968 A226158 A024040 * A338489 A009759 A127187

Adjacent sequences: A357808 A357809 A357810 * A357812 A357813 A357814

KEYWORD

nonn,easy,walk

AUTHOR

Dave R.M. Langers, Oct 13 2022

STATUS

approved