A323188 Number of n-step mirror-symmetrical self-avoiding walks on the square lattice.

4, 12, 12, 28, 28, 76, 76, 188, 196, 516, 524, 1292, 1356, 3500, 3596, 8908, 9380, 23940, 24796, 61500, 64900, 164612, 171244, 424940, 449140, 1134772, 1184204, 2939212, 3109644, 7834764, 8196100, 20345316, 21539420, 54156316, 56762036, 140908948, 149255908

Offset: 1

Author

Bert Dobbelaere, Jan 06 2019

Keywords

• nonn
• walk

Comments

Total number of walks as counted in A001411 that have an axis of symmetry, either parallel to an axis or at a 45-degree angle (the latter only possible for even n).

Links

• Bert Dobbelaere, Table of n, a(n) for n = 1..60
• Bert Dobbelaere, Illustration of initial terms
• Brian Hayes, How to avoid yourself, American Scientist 86 (1998) 314-319.

Crossrefs

Cf. A001411, A037245, A151538, A316194, A323189 (program).

Programs

Mathematica

A037245 = Import["https://oeis.org/A037245/b037245.txt", "Table"][[All, 2]];
A151538 = Import["https://oeis.org/A151538/b151538.txt", "Table"][[All, 2]];
a[n_] := 16 A037245[[n]] - 8 A151538[[n]] - 4;
Array[a, 60] (* Jean-François Alcover, Sep 17 2019 *)

Formula

A037245(n) = (A001411(n) + a(n) + A323189(n) + 4) / 16.