cp's OEIS Frontend

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.

%I A259857 #26 Apr 05 2020 09:46:44
%S A259857 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 A259857 0,0,0,6,134,676,1868,0,0,0,0,1,72,656,2672,6237,0,0,0,0,0,30,482,
%U A259857 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 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.
%H A259857 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 A259857 Triangle begins:
%e A259857 ==========================================================
%e A259857 n\k  | 2 3 4  5  6   7   8    9    10    11     12     13
%e A259857 -----|----------------------------------------------------
%e A259857    1 | 1,
%e A259857    2 | 0,2,
%e A259857    3 | 0,0,6,
%e A259857    4 | 0,0,1,18
%e A259857    5 | 0,0,0, 8,55,
%e A259857    6 | 0,0,0, 2,40,174,
%e A259857    7 | 0,0,0, 0,22,168,566,
%e A259857    8 | 0,0,0, 0, 6,134,676,1868,
%e A259857    9 | 0,0,0, 0, 1, 72,656,2672, 6237,
%e A259857   10 | 0,0,0, 0, 0, 30,482,2992,10376,21050,
%e A259857   11 | 0,0,0, 0, 0,  8,310,2592,13160,39824, 71666,
%e A259857   12 | 0,0,0, 0, 0,  2,151,2086,12862,56162,151878,245696,
%Y A259857 A006725 and A006726 are diagonals.
%Y A259857 Row sums give A006724.
%Y A259857 Cf. A008855 (with 0 omitted).
%K A259857 nonn,tabl
%O A259857 1,3
%A A259857 _N. J. A. Sloane_, Jul 07 2015
%E A259857 a(7)-a(10) inserted by _Seiichi Manyama_, Apr 04 2020