A338211 Triangle of coefficients of perimeter polynomials for free polyominoes.

1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 5, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 11, 10, 10, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 18, 37, 30, 15, 3, 1

Offset: 0

Author

Sean A. Irvine, Oct 17 2020

Keywords

• nonn
• tabf

Comments

Considered as a triangle, T(n,k) is the number of free polyominoes of n cells having a (cell) perimeter of k.

Examples

			Polynomials begin:
  1;
  x^4;
  x^6;
  x^7 + x^8;
  3*x^8 + x^9 + x^10;
  ...
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 0..437; rows 0..19 flattened
• Sean A. Irvine, Java program (github)

Crossrefs

Cf. A000105 (row sums), A338210 (fixed equivalent), A338213 (sprawl), A366443 (column sums).

Formula

A000105(n) = Sum_{k=0..2*n+2} T(n,k).