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, 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

Offset: 1

Author

N. J. A. Sloane, Jul 07 2015

Keywords

• nonn
• tabl

Examples

			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,
		

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.

Crossrefs

A006725 and A006726 are diagonals.

Row sums give A006724.

Cf. A008855 (with 0 omitted).

Extensions

a(7)-a(10) inserted by Seiichi Manyama, Apr 04 2020