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.

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

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%I A323188 #24 Feb 26 2025 08:02:24
%S A323188 4,12,12,28,28,76,76,188,196,516,524,1292,1356,3500,3596,8908,9380,
%T A323188 23940,24796,61500,64900,164612,171244,424940,449140,1134772,1184204,
%U A323188 2939212,3109644,7834764,8196100,20345316,21539420,54156316,56762036,140908948,149255908
%N A323188 Number of n-step mirror-symmetrical self-avoiding walks on the square lattice.
%C A323188 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).
%H A323188 Bert Dobbelaere, <a href="/A323188/b323188.txt">Table of n, a(n) for n = 1..60</a>
%H A323188 Bert Dobbelaere, <a href="/A323188/a323188.pdf">Illustration of initial terms</a>
%H A323188 Brian Hayes, <a href="https://www.americanscientist.org/article/how-to-avoid-yourself">How to avoid yourself</a>, American Scientist 86 (1998) 314-319.
%F A323188 A037245(n) = (A001411(n) + a(n) + A323189(n) + 4) / 16.
%t A323188 A037245 = Import["https://oeis.org/A037245/b037245.txt", "Table"][[All, 2]];
%t A323188 A151538 = Import["https://oeis.org/A151538/b151538.txt", "Table"][[All, 2]];
%t A323188 a[n_] := 16 A037245[[n]] - 8 A151538[[n]] - 4;
%t A323188 Array[a, 60] (* _Jean-François Alcover_, Sep 17 2019 *)
%Y A323188 Cf. A001411, A037245, A151538, A316194, A323189 (program).
%K A323188 nonn,walk
%O A323188 1,1
%A A323188 _Bert Dobbelaere_, Jan 06 2019