A006781 -id:A006781 - cp's OEIS frontend

A006782 Number of polygons of length 4n on L-lattice.

1, 0, 1, 2, 9, 36, 154, 684, 3128, 14666, 70258, 342766, 1698625, 8532410, 43368153, 222729492, 1154455161, 6033034032, 31760434883, 168311948410, 897327111964, 4810159375532, 25914118276362

Offset: 1

N. J. A. Sloane

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Thorsten Ehlers, (C) simple generation algorithm
I. G. Enting and A. J. Guttmann, Self-avoiding polygons on the square, L and Manhattan lattices, J. Phys. A 18 (1985), 1007-1017.
Sean A. Irvine, Java program (github)

Cf. A002931, A006781.

a(13)-a(15) from Sean A. Irvine, Aug 01 2017
a(16)-a(21) from Thorsten Ehlers, Sep 30 2018
a(22) from Thorsten Ehlers, Nov 01 2018
a(23) from Thorsten Ehlers, Apr 16 2019

A336742 Number of self-avoiding cycles of length 2n on the half-Manhattan lattice.

Original entry on oeis.org

1, 0, 1, 1, 2, 6, 17, 49, 156, 520, 1762, 6110, 21713, 78469, 287393, 1065951, 3998286, 15140500, 57817817, 222478829, 861952579, 3360043843, 13171307962

Offset: 0

Sean A. Irvine, Aug 02 2020

In the half-Manhattan lattice, E-W streets run alternately E and W, but N-S streets are two way.

Sean A. Irvine, Java program (github)

Cf. A336724 (self-avoiding walks), A006781 (Manhattan lattice), A006782 (L-lattice), A002931 (square lattice).

cp's OEIS Frontend

A006782 Number of polygons of length 4n on L-lattice.

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