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A268371 Triangle read by rows: T(n,k) is the number of free polyominoes with width n and height 1<=k<=n.

%I A268371 #42 Mar 21 2024 21:04:19
%S A268371 1,1,2,1,6,24,1,12,181,1051,1,30,941,21992,238048,1,65,4662,228013,
%T A268371 9735647,195284973,1,158,23691,2337694,195616247,15256715219,
%U A268371 577169894573
%N A268371 Triangle read by rows: T(n,k) is the number of free polyominoes with width n and height 1<=k<=n.
%C A268371 Superset of Craig Knecht's A268311.
%H A268371 Jean-Luc Manguin, <a href="/A268371/b268371.txt">Table of n, a(n) for n = 1..28</a>
%H A268371 R. J. Mathar, <a href="http://www.vixra.org/abs/1905.0474">Corrigendum to "Polyomino Enumeration Results (Parkin et al, SIAM Fall Meeting 1967)"</a> viXra:1905.0474 (2019)
%H A268371 R. Parkin, L. J. Lander, and D. R. Parkin, <a href="/A000104/a000104.pdf">Polyomino Enumeration Results</a>, presented at SIAM Fall Meeting, 1967, and accompanying letter from T. J. Lander (annotated scanned copy) page 9 (incorrect at n=15).
%H A268371 <a href="/index/Pol#polyominoes">Index entries for sequences related to polyominoes</a>
%e A268371 The first rows of the array are:
%e A268371 1;
%e A268371 1, 2;
%e A268371 1, 6, 24;
%e A268371 1, 12, 181, 1051;
%e A268371 ...
%e A268371 T(4,3)=181 = 15+39+59+42+21+4+1: In the 4x3 square fit 15 6-ominoes, 39 7-ominoes, 59 8-ominoes, 42 9-ominoes, 21 10-ominoes, 4 11-ominoes or 1 12-omino. - _R. J. Mathar_, Jun 07 2020
%Y A268371 Cf. A268311 (right diagonal), A335711 (column n=2), A000105 (free polyominoes), A292357 (equival. for fixed polys).
%K A268371 nonn,tabl,more
%O A268371 1,3
%A A268371 _John Mason_, Feb 03 2016
%E A268371 a(16)-a(28) from _Jean-Luc Manguin_, May 25 2020