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%I #31 Apr 05 2020 02:41:02
%S 1,2,6,1,18,8,55,2,40,174,22,168,566,6,134,676,1868,1,72,656,2672,
%T 6237,30,482,2992,10376,21050,8,310,2592,13160,39824,71666,2,151,2086,
%U 12862,56162,151878,245696,68,1392,11717,61032,234520,576656,847317,22,864,9332,60864,279492,965136,2181496,2937116
%N Triangle T(n,k), n>=1, read by rows, where T(n,k) is the number of lattice polygons with area n and perimeter 2*k.
%C Row lengths are 1, 1, 1, 2, 2, 3, 3, 4, 5, 5, ...
%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.
%e T(1,2) = 1;
%e +--+
%e | |
%e +--+
%e T(2,3) = 2;
%e +--+
%e | |
%e +--+ +--+--+
%e | | | | |
%e +--+ +--+--+
%e T(3,4) = 6;
%e +--+
%e | |
%e +--+ +--+
%e | | | |
%e +--+ +--+--+--+ +--+--+
%e | | | | | | | | |
%e +--+ +--+--+--+ +--+--+
%e +--+ +--+--+ +--+--+
%e | | | | | | | |
%e +--+--+ +--+--+ +--+--+
%e | | | | | | |
%e +--+--+ +--+ +--+
%e ============================================
%e n\k | 2 3 4 5 6 7 8 9 10
%e ----|---------------------------------------
%e 1 | 1;
%e 2 | 2;
%e 3 | 6;
%e 4 | 1, 18;
%e 5 | 8, 55;
%e 6 | 2, 40, 174;
%e 7 | 22, 168, 566;
%e 8 | 6, 134, 676, 1868;
%e 9 | 1, 72, 656, 2672, 6237;
%Y Cf. A006725, A006726, A259857.
%K nonn,tabf,nice
%O 1,2
%A _N. J. A. Sloane_
%E More terms from _Sean A. Irvine_, Apr 12 2018
%E Examples added and name edited by _Seiichi Manyama_, Apr 04 2020
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