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A259857 Triangle T(n,k), n>=1, 2<=k<=n+1, read by rows, where T(n,k) is the number of self-avoiding square-lattice polygons by area n and perimeter 2*k. 1
1, 0, 2, 0, 0, 6, 0, 0, 1, 18, 0, 0, 0, 8, 55, 0, 0, 0, 2, 40, 174, 0, 0, 0, 0, 22, 168, 566, 0, 0, 0, 0, 6, 134, 676, 1868, 0, 0, 0, 0, 1, 72, 656, 2672, 6237, 0, 0, 0, 0, 0, 30, 482, 2992, 10376, 21050, 0, 0, 0, 0, 0, 8, 310, 2592, 13160, 39824, 71666, 0, 0, 0, 0, 0, 2, 151, 2086, 12862, 56162, 151878, 245696 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
I. G. Enting and A. J. Guttmann, On the area of square lattice polygons, J. Statist. Phys., 58 (1990), 475-484. See Table 1.
EXAMPLE
Triangle begins:
==========================================================
n\k | 2 3 4 5 6 7 8 9 10 11 12 13
-----|----------------------------------------------------
1 | 1,
2 | 0,2,
3 | 0,0,6,
4 | 0,0,1,18
5 | 0,0,0, 8,55,
6 | 0,0,0, 2,40,174,
7 | 0,0,0, 0,22,168,566,
8 | 0,0,0, 0, 6,134,676,1868,
9 | 0,0,0, 0, 1, 72,656,2672, 6237,
10 | 0,0,0, 0, 0, 30,482,2992,10376,21050,
11 | 0,0,0, 0, 0, 8,310,2592,13160,39824, 71666,
12 | 0,0,0, 0, 0, 2,151,2086,12862,56162,151878,245696,
CROSSREFS
A006725 and A006726 are diagonals.
Row sums give A006724.
Cf. A008855 (with 0 omitted).
Sequence in context: A181229 A364233 A364230 * A364790 A094785 A265856
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Jul 07 2015
EXTENSIONS
a(7)-a(10) inserted by Seiichi Manyama, Apr 04 2020
STATUS
approved

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Last modified July 18 06:54 EDT 2024. Contains 374377 sequences. (Running on oeis4.)