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A323189 Number of n-step point-symmetrical self-avoiding walks on the square lattice. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 27 12:24 EST 2023. Contains 359840 sequences. (Running on oeis4.)