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A121769 Number of neighbor-avoiding polygons of perimeter 2n on square lattice. 1
0, 1, 0, 1, 2, 9, 36, 154, 668, 2932, 13016, 58364, 264208, 1206818, 5558724, 25803509, 120638466, 567732133, 2687937916, 12796823923, 61235363802, 294407424869, 1421635103832, 6892590800146, 33543439104796 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Bennett-Wood et al. (1998) used the notation p_n(k) "for the numbers of SAPs of length n with k-nearest-neighbour contacts" and they calculated them up to n=42. (Here, SAP = self-avoiding polygon.) In Table A1 of their paper (pp. 4736-4737), they calculate p_n(k) for n = 4,6,..., 40, 42 (even only) and all possible k's. It turns out that for the current sequence a(m) = p_{2*m}(k=0) for m >= 1. (Thus, Table B1 of Bennett-Wood et al. (1998) has no entries for p_n(k) when n is odd.) - Petros Hadjicostas, Jan 05 2019

LINKS

I. Jensen, Table of n, a(n) for n = 1..43 (from link below)

D. Bennett-Wood, I. G. Enting, D. S. Gaunt, A. J. Guttmann, J. L. Leask, A. L. Owczarek, and S. G. Whittington, Exact enumeration study of free energies of interacting polygons and walks in two dimensions, J. Phys. A: Math. Gen. 31 (1998), 4725-4741.

I. Jensen, More terms [Archived link, first column has the perimeter (4, 6, 8, ...)]

CROSSREFS

Sequence in context: A052834 A289805 A150967 * A006782 A150968 A073156

Adjacent sequences:  A121766 A121767 A121768 * A121770 A121771 A121772

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Aug 30 2006

STATUS

approved

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Last modified September 25 12:23 EDT 2020. Contains 337343 sequences. (Running on oeis4.)