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A323188
Number of n-step mirror-symmetrical self-avoiding walks on the square lattice.
4
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
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
Sequence in context: A211437 A195199 A294628 * A284126 A272841 A272942
KEYWORD
nonn,walk
AUTHOR
Bert Dobbelaere, Jan 06 2019
STATUS
approved