A342243 Triangle T(n,p) read by rows: the number of n-celled polyominoes with perimeter 2p, 2 <= p <= 1+n.

1, 0, 1, 0, 0, 2, 0, 0, 1, 4, 0, 0, 0, 1, 11, 0, 0, 0, 1, 7, 27, 0, 0, 0, 0, 4, 21, 83, 0, 0, 0, 0, 2, 21, 91, 255, 0, 0, 0, 0, 1, 9, 89, 339, 847, 0, 0, 0, 0, 0, 6, 67, 393, 1360, 2829, 0, 0, 0, 0, 0, 1, 45, 325, 1713, 5255, 9734, 0, 0, 0, 0, 0, 1, 23, 275

Offset

1,6

Links

John Mason, Table of T(n,k) for n <= 18 (n <= 17 from R. J. Mathar)

Andrew Clarke, Isoperimetrical Polyominoes

John Mason, Incomplete rows for n>18

Formula

A131487(e) = Sum_{e=2*n+p} T(n,p).

Example

The triangle has rows n=1,2,3,... and columns p=2,3,4,5,...:
  1;
  0, 1;
  0, 0, 2;
  0, 0, 1, 4;
  0, 0, 0, 1, 11;
  0, 0, 0, 1,  7, 27;
  0, 0, 0, 0,  4, 21, 83;
  0, 0, 0, 0,  2, 21, 91, 255;
  0, 0, 0, 0,  1,  9, 89, 339,  847;
  0, 0, 0, 0,  0,  6, 67, 393, 1360, 2829;
  0, 0, 0, 0,  0,  1, 45, 325, 1713, 5255, 9734;
  ...

Crossrefs

Cf. A000105 (row sums), A057730 (column sums), A131482 (diagonal), A131487 (skew antidiagonal sums), A027709 (number of leading zeros per row), A100092 (first nonzero in each row).

Sequence in context: A259784 A145224 A138157 * A073429 A123634 A330140

Adjacent sequences: A342240 A342241 A342242 * A342244 A342245 A342246

Keyword

nonn,tabl,hard

Author

R. J. Mathar, Mar 07 2021

Status

approved