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A338211 Triangle of coefficients of perimeter polynomials for free polyominoes. 3
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 (list; graph; refs; listen; history; text; internal format)
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 A115718

Adjacent sequences:  A338208 A338209 A338210 * A338212 A338213 A338214

KEYWORD

nonn,tabf

AUTHOR

Sean A. Irvine, Oct 17 2020

STATUS

approved

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Last modified March 5 16:55 EST 2021. Contains 341827 sequences. (Running on oeis4.)