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Triangle of coefficients of perimeter polynomials for fixed polyominoes.
4

%I #10 Oct 19 2020 06:00:10

%S 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,

%T 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,

%U 0,0,0,0,0,0,22,136,252,228,100,20,2

%N Triangle of coefficients of perimeter polynomials for fixed polyominoes.

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

%H Sean A. Irvine, <a href="/A338210/b338210.txt">Table of n, a(n) for n = 0..437; rows 0..19 flattened</a>

%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a338/A338210.java">Java program</a> (github)

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

%e Polynomials begin:

%e 1;

%e x^4;

%e 2*x^6;

%e 4*x^7 + 2*x^8;

%e 9*x^8 + 8*x^9 + 2*x^10;

%e ...

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

%K nonn,tabf

%O 0,13

%A _Sean A. Irvine_, Oct 16 2020