cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A359133 Sum of square end-to-end displacements over all n-step self-avoiding walks of A359741.

Original entry on oeis.org

0, 6, 24, 78, 384, 8190, 8472, 178110, 193824, 4231662, 7072056, 102812142, 208526592, 2508914454, 5268441144, 62304671286, 124116667488, 1547651742990, 2850706506936, 38100453950670
Offset: 0

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Author

Scott R. Shannon, Jan 12 2023

Keywords

Crossrefs

A359709 Number of n-step self-avoiding walks on a 2D square lattice whose end-to-end distance is an integer.

Original entry on oeis.org

1, 4, 4, 12, 28, 76, 164, 732, 1044, 4924, 6724, 30636, 43972, 190516, 313996, 1197908, 2284260, 7678188, 16257604, 50524252, 113052396, 341811828, 773714436, 2358452388, 5245994292, 16447462492, 35395532236, 115129727188, 238542983748, 804980005276
Offset: 0

Views

Author

Scott R. Shannon, Jan 12 2023

Keywords

Comments

The walks counted are all those directly along and x or y axes, and all walks whose final (|x|,|y|) lattice point are the two legs of a Pythagorean triple.

Examples

			a(3) = 12 as, in the first quadrant, there is one 3-step SAW whose end-to-end distance is an integer (1 unit):
.
     X---.
         |
     X---.
.
This can be walked in 8 different ways on a 2D square lattice. There are also the four walks directly along the x and y axes, giving a total of 8 + 4 = 12 walks.
		

Crossrefs

Showing 1-2 of 2 results.