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.

1, 2, 6, 1, 18, 8, 55, 2, 40, 174, 22, 168, 566, 6, 134, 676, 1868, 1, 72, 656, 2672, 6237, 30, 482, 2992, 10376, 21050, 8, 310, 2592, 13160, 39824, 71666, 2, 151, 2086, 12862, 56162, 151878, 245696, 68, 1392, 11717, 61032, 234520, 576656, 847317, 22, 864, 9332, 60864, 279492, 965136, 2181496, 2937116

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• tabf
• nice

Comments

Row lengths are 1, 1, 1, 2, 2, 3, 3, 4, 5, 5, ...

Examples

			T(1,2) = 1;
   +--+
   |  |
   +--+
T(2,3) = 2;
   +--+
   |  |
   +--+   +--+--+
   |  |   |  |  |
   +--+   +--+--+
T(3,4) = 6;
   +--+
   |  |
   +--+                +--+
   |  |                |  |
   +--+   +--+--+--+   +--+--+
   |  |   |  |  |  |   |  |  |
   +--+   +--+--+--+   +--+--+
      +--+   +--+--+   +--+--+
      |  |   |  |  |   |  |  |
   +--+--+   +--+--+   +--+--+
   |  |  |   |  |         |  |
   +--+--+   +--+         +--+
============================================
n\k | 2  3  4   5   6    7    8     9    10
----|---------------------------------------
  1 | 1;
  2 |    2;
  3 |       6;
  4 |       1, 18;
  5 |           8, 55;
  6 |           2, 40, 174;
  7 |              22, 168, 566;
  8 |               6, 134, 676, 1868;
  9 |               1,  72, 656, 2672, 6237;
		

Links

• Andrey Zabolotskiy, Table of n, a(n) for n = 1..120 (rows 1..20, from Enting & Guttmann)
• I. G. Enting and A. J. Guttmann, On the area of square lattice polygons, J. Statist. Phys., 58 (1990), 475-484.

Crossrefs

Cf. A006725, A006726, A259857.

Extensions

More terms from Sean A. Irvine, Apr 12 2018

Examples added and name edited by Seiichi Manyama, Apr 04 2020