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

0,31

Comments

Considered as a triangle, T(n,k) is the number of free 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

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

Example

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

Crossrefs

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

Sequence in context: A066746 A278105 A074063 * A115717 A339632 A350879

Adjacent sequences: A338208 A338209 A338210 * A338212 A338213 A338214

Keyword

nonn,tabf

Author

Sean A. Irvine, Oct 17 2020

Status

approved