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

1,1

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.

Formula

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

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 *)

Crossrefs

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

Sequence in context: A211437 A195199 A294628 * A284126 A272841 A272942

Adjacent sequences: A323185 A323186 A323187 * A323189 A323190 A323191

Keyword

nonn,walk

Author

Bert Dobbelaere, Jan 06 2019

Status

approved