A357810 Number of n-step closed paths on the Cairo pentagonal lattice graph starting from a degree-4 node.

1, 0, 4, 0, 24, 8, 164, 136, 1236, 1704, 10116, 19144, 88616, 205208, 818764, 2155160, 7873440, 22463400, 77954740, 233894600, 788314984, 2440865400, 8095906076, 25569342520, 84107990356, 269034666280

Offset

0,3

Links

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

Wikipedia, Cairo pentagonal tiling

Example

For n=2, the a(2) = 4 solutions visit one of the four vertices adjacent to the initial vertex, and then return.
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.

Crossrefs

The accompanying sequences for the number of paths that return to a degree-3 node is A357811.

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

Sequence in context: A243270 A242027 A329891 * A057402 A269214 A269276

Adjacent sequences: A357807 A357808 A357809 * A357811 A357812 A357813

Keyword

nonn,easy,walk

Author

Dave R.M. Langers, Oct 13 2022

Status

approved