A338213 -id:A338213 - cp's OEIS frontend

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

Sean A. Irvine, Oct 17 2020

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

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

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

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

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

A338212 a(n) is the number of fixed polyominoes with sprawl n.

Original entry on oeis.org

1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 4, 2, 9, 9, 22, 32, 66, 104, 200, 348, 646, 1172, 2144, 3964, 7285, 13581, 25136, 47070, 87700, 164764, 309308, 582152, 1098698, 2074484

Offset: 0

Sean A. Irvine and Allan C. Wechsler, Oct 17 2020

The sprawl of a polyomino is the number of cells in a polyomino plus the number of cells adjacent to it.

Sean A. Irvine, Java program (github)

Cf. A001168, A338210, A338213.

Antidiagonal sums of A338210.

cp's OEIS Frontend

A338211 Triangle of coefficients of perimeter polynomials for free polyominoes.

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