A259857 - OEIS

%I #26 Apr 05 2020 09:46:44

%S 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,

%T 0,0,0,6,134,676,1868,0,0,0,0,1,72,656,2672,6237,0,0,0,0,0,30,482,

%U 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

%N 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.

%H I. G. Enting and A. J. Guttmann, <a href="http://dx.doi.org/10.1007/BF01112757">On the area of square lattice polygons</a>, J. Statist. Phys., 58 (1990), 475-484. See Table 1.

%e Triangle begins:

%e ==========================================================

%e n\k  | 2 3 4  5  6   7   8    9    10    11     12     13

%e -----|----------------------------------------------------

%e    1 | 1,

%e    2 | 0,2,

%e    3 | 0,0,6,

%e    4 | 0,0,1,18

%e    5 | 0,0,0, 8,55,

%e    6 | 0,0,0, 2,40,174,

%e    7 | 0,0,0, 0,22,168,566,

%e    8 | 0,0,0, 0, 6,134,676,1868,

%e    9 | 0,0,0, 0, 1, 72,656,2672, 6237,

%e   10 | 0,0,0, 0, 0, 30,482,2992,10376,21050,

%e   11 | 0,0,0, 0, 0,  8,310,2592,13160,39824, 71666,

%e   12 | 0,0,0, 0, 0,  2,151,2086,12862,56162,151878,245696,

%Y A006725 and A006726 are diagonals.

%Y Row sums give A006724.

%Y Cf. A008855 (with 0 omitted).

%K nonn,tabl

%O 1,3

%A _N. J. A. Sloane_, Jul 07 2015

%E a(7)-a(10) inserted by _Seiichi Manyama_, Apr 04 2020