A323189 Number of n-step point-symmetrical self-avoiding walks on the square lattice.

4, 4, 12, 12, 36, 36, 100, 100, 284, 276, 780, 764, 2148, 2084, 5868, 5692, 15956, 15436, 43300, 41812, 117100, 112916, 316076, 304524, 851612, 819372, 2290932, 2203132, 6154284, 5912572, 16514988, 15859820, 44268460, 42480972, 118562580, 113738396, 317268516

Offset

1,1

Comments

Total number of walks as counted in A001411 that have a point of symmetry.

Note that for k > 4, we observe a(2k) < a(2k-1). This can be understood by considering interference between the parts at both sides of the point of symmetry (see illustration).

Links

Bert Dobbelaere, Table of n, a(n) for n = 1..60

Bert Dobbelaere, Illustration of initial terms

Bert Dobbelaere, C++ program

Brian Hayes, How to avoid yourself, American Scientist 86 (1998) 314-319.

Formula

A037245(n) = (A001411(n) + A323188(n) + a(n) + 4) / 16.

A151538(n) = (A001411(n) + a(n)) / 8.

Mathematica

A001411 = Import["https://oeis.org/A001411/b001411.txt", "Table"][[All, 2]];
A151538 = Import["https://oeis.org/A151538/b151538.txt", "Table"][[All, 2]];
a[n_] := 8 A151538[[n]] - A001411[[n+2]];
Array[a, 60] (* Jean-François Alcover, Sep 17 2019 *)

Crossrefs

Cf. A001411, A037245, A151538, A316194, A323188.

Sequence in context: A281913 A178776 A282503 * A121189 A136485 A157617

Adjacent sequences: A323186 A323187 A323188 * A323190 A323191 A323192

Keyword

nonn,walk

Author

Bert Dobbelaere, Jan 06 2019

Status

approved