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A338211 Triangle of coefficients of perimeter polynomials for free polyominoes.

%I A338211 #13 Apr 14 2025 11:02:29
%S A338211 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,
%T A338211 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,
%U A338211 0,0,0,0,4,18,37,30,15,3,1
%N A338211 Triangle of coefficients of perimeter polynomials for free polyominoes.
%C A338211 Considered as a triangle, T(n,k) is the number of free polyominoes of n cells having a (cell) perimeter of k.
%H A338211 Sean A. Irvine, <a href="/A338211/b338211.txt">Table of n, a(n) for n = 0..437; rows 0..19 flattened</a>
%H A338211 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a338/A338211.java">Java program</a> (github)
%F A338211 A000105(n) = Sum_{k=0..2*n+2} T(n,k).
%e A338211 Polynomials begin:
%e A338211   1;
%e A338211   x^4;
%e A338211   x^6;
%e A338211   x^7 + x^8;
%e A338211   3*x^8 + x^9 + x^10;
%e A338211   ...
%Y A338211 Cf. A000105 (row sums), A338210 (fixed equivalent), A338213 (sprawl), A366443 (column sums).
%K A338211 nonn,tabf
%O A338211 0,31
%A A338211 _Sean A. Irvine_, Oct 17 2020