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

1,2

Comments

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

Links

Table of n, a(n) for n=1..55.

I. G. Enting and A. J. Guttmann, On the area of square lattice polygons, J. Statist. Phys., 58 (1990), 475-484.

Example

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;

Crossrefs

Cf. A006725, A006726, A259857.

Sequence in context: A281417 A175353 A181307 * A345043 A181299 A181365

Adjacent sequences: A008852 A008853 A008854 * A008856 A008857 A008858

Keyword

nonn,tabf,nice

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Apr 12 2018

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

Status

approved