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.

Showing 1-3 of 3 results.

A359073 Sum of square end-to-end displacements over all n-step self-avoiding walks of A359709.

Original entry on oeis.org

0, 4, 16, 44, 160, 556, 1744, 12252, 15840, 98876, 138160, 709900, 1155616, 5098260, 11820656, 37085908, 111147104, 281078764, 932893104, 2255139900, 7295211968, 18928121236, 54864568720, 160016686500, 404167501888, 1331607134172, 2945597090384, 10805511468852, 21448743511648
Offset: 0

Views

Author

Scott R. Shannon, Jan 12 2023

Keywords

Crossrefs

Cf. A359709, A103606, A359133, A336448, A001411, A356617, A173380, A337353, A358036, A358046.

A358083 Sum of square end-to-end displacements over all n-step self-avoiding walks of A358046.

Original entry on oeis.org

4, 16, 128, 448, 2256, 5376, 29424, 69888, 302568, 741376, 3026448, 7216896, 29268352, 65785216, 263892736, 591065568, 2279452040, 5195776064, 19324558176, 44442289024, 161417689504, 371206519136, 1328055630144, 3044451252064, 10774811055304, 24625495784320, 86363375773808, 197092099990080
Offset: 1

Views

Author

Scott R. Shannon, Oct 30 2022

Keywords

Comments

See A358046 for further details.

Examples

			a(3) = 128 as, in the first quadrant, the four 3-step SAWs that have the first and last visited lattice point being mutually visible are:
.
                  X
                  |
     X---.        .          .---X           X
         |        |          |               |
     X---.    X---.      X---.       X---.---.
.
The sum of square end-to-end displacements of these four walks is 1 + 5 + 5 + 5 = 16. They can be walked in eight different ways on a square lattice thus a(3) = 16 * 8 = 128.

Crossrefs

Cf. A358046, A358084, A001411, A336448.

A358084 Sum of square end-to-end displacements over all n-step self-avoiding walks of A358036.

Original entry on oeis.org

0, 16, 88, 288, 1104, 3264, 12032, 34144, 115112, 323888, 1043360, 2903280, 9122592, 24993552, 77246888, 209811360, 637734248, 1726546928, 5170075216, 13965402144, 41331646184, 111361083152, 326576770784, 877687158464, 2554653282056, 6850500549888, 19812687702472, 53030550412576
Offset: 1

Views

Author

Scott R. Shannon, Oct 30 2022

Keywords

Comments

See A358036 for further details.

Examples

			a(3) = 88 as, in the first quadrant, the three 3-step SAWs that have the first and last visited lattice point being mutually visible are:
.
                  X
                  |
     X---.        .            X
         |        |            |
     X---.    X---.    X---.---.
.
The sum of square end-to-end displacements of these three walks is 1 + 5 + 5 = 11. They can be walked in eight different ways on a square lattice thus a(3) = 11 * 8 = 88.

Crossrefs

Cf. A358036, A358083, A001411, A336448.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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