cp's OEIS Frontend

A008855 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.

%I A008855 #40 Sep 28 2024 10:42:08
%S A008855 1,2,6,1,18,8,55,2,40,174,22,168,566,6,134,676,1868,1,72,656,2672,
%T A008855 6237,30,482,2992,10376,21050,8,310,2592,13160,39824,71666,2,151,2086,
%U A008855 12862,56162,151878,245696,68,1392,11717,61032,234520,576656,847317,22,864,9332,60864,279492,965136,2181496,2937116
%N A008855 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 A008855 Row lengths are 1, 1, 1, 2, 2, 3, 3, 4, 5, 5, ...
%H A008855 Andrey Zabolotskiy, <a href="/A008855/b008855.txt">Table of n, a(n) for n = 1..120</a> (rows 1..20, from Enting & Guttmann)
%H A008855 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 A008855 T(1,2) = 1;
%e A008855    +--+
%e A008855    |  |
%e A008855    +--+
%e A008855 T(2,3) = 2;
%e A008855    +--+
%e A008855    |  |
%e A008855    +--+   +--+--+
%e A008855    |  |   |  |  |
%e A008855    +--+   +--+--+
%e A008855 T(3,4) = 6;
%e A008855    +--+
%e A008855    |  |
%e A008855    +--+                +--+
%e A008855    |  |                |  |
%e A008855    +--+   +--+--+--+   +--+--+
%e A008855    |  |   |  |  |  |   |  |  |
%e A008855    +--+   +--+--+--+   +--+--+
%e A008855       +--+   +--+--+   +--+--+
%e A008855       |  |   |  |  |   |  |  |
%e A008855    +--+--+   +--+--+   +--+--+
%e A008855    |  |  |   |  |         |  |
%e A008855    +--+--+   +--+         +--+
%e A008855 ============================================
%e A008855 n\k | 2  3  4   5   6    7    8     9    10
%e A008855 ----|---------------------------------------
%e A008855   1 | 1;
%e A008855   2 |    2;
%e A008855   3 |       6;
%e A008855   4 |       1, 18;
%e A008855   5 |           8, 55;
%e A008855   6 |           2, 40, 174;
%e A008855   7 |              22, 168, 566;
%e A008855   8 |               6, 134, 676, 1868;
%e A008855   9 |               1,  72, 656, 2672, 6237;
%Y A008855 Cf. A006725, A006726, A259857.
%K A008855 nonn,tabf,nice
%O A008855 1,2
%A A008855 _N. J. A. Sloane_
%E A008855 More terms from _Sean A. Irvine_, Apr 12 2018
%E A008855 Examples added and name edited by _Seiichi Manyama_, Apr 04 2020