

A121769


Number of neighboravoiding 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

BennettWood et al. (1998) used the notation p_n(k) "for the numbers of SAPs of length n with knearestneighbour contacts" and they calculated them up to n=42. (Here, SAP = selfavoiding polygon.) In Table A1 of their paper (pp. 47364737), 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 BennettWood 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. BennettWood, 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), 47254741.
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



