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

0,13

Comments

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

Links

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

Sean A. Irvine, Java program (github)

Formula

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

Example

Polynomials begin:
  1;
  x^4;
  2*x^6;
  4*x^7 + 2*x^8;
  9*x^8 + 8*x^9 + 2*x^10;
  ...

Crossrefs

Cf. A001168 (row sums), A338211 (free equivalent), A338212 (sprawl), A003203.

Sequence in context: A182660 A286100 A359431 * A122698 A002483 A282530

Adjacent sequences: A338207 A338208 A338209 * A338211 A338212 A338213

Keyword

nonn,tabf

Author

Sean A. Irvine, Oct 16 2020

Status

approved