A338210 Triangle of coefficients of perimeter polynomials for fixed polyominoes.

1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 9, 8, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 20, 28, 12, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 54, 80, 60, 16, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22, 136, 252, 228, 100, 20, 2

Offset: 0

Author

Sean A. Irvine, Oct 16 2020

Keywords

• nonn
• tabf

Comments

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

Examples

			Polynomials begin:
  1;
  x^4;
  2*x^6;
  4*x^7 + 2*x^8;
  9*x^8 + 8*x^9 + 2*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. A001168 (row sums), A338211 (free equivalent), A338212 (sprawl), A003203.

Formula

A001168(n) = Sum_{k=0..2*n+2} T(n,k).