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A126743 Triangle read by rows: T(n,k) (n>=1) gives the number of n-indecomposable polyominoes with k cells (k >= 2n).

%I A126743 #9 Jan 23 2019 20:01:13
%S A126743 0,0,0,0,1,1,0,0,0,0,0,6,5,1,1,0,0,0,0,0,0,0,73,76,80,25,15,15,0,0,0,
%T A126743 0,0,0,0,0,0,1044,1475,2205,2643,983,1050,1208,958,0,0,0,0,0,0,0,0,0,
%U A126743 0,0,15980,26548,48766,79579,99860,45898,60433,89890,109424,84312,0,0,0,0,0,0,0,0,0,0,0,0,0,245955,458397,948201,1857965,3160371,4153971,2217787,3402761,5855953,9067535,11402651,9170285,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3807508,7710844,17354771,37983463
%N A126743 Triangle read by rows: T(n,k) (n>=1) gives the number of n-indecomposable polyominoes with k cells (k >= 2n).
%C A126743 A polyomino is called n-indecomposable if it cannot be partitioned (along cell boundaries) into two or more polyominoes each with at least n cells.
%C A126743 Row n has 4n-3 terms of which the first 2n-1 are zero.
%C A126743 For full lists of drawings of these polyominoes for n <= 6, see the links in A125759.
%H A126743 N. MacKinnon, <a href="http://www.jstor.org/stable/3618845">Some thoughts on polyomino tilings</a>, Math. Gaz., 74 (1990), 31-33.
%H A126743 Simone Rinaldi and D. G. Rogers, <a href="http://www.jstor.org/stable/27821767">Indecomposability: polyominoes and polyomino tilings</a>, The Mathematical Gazette 92.524 (2008): 193-204.
%e A126743 Triangle begins:
%e A126743 0
%e A126743 0,0,0,1,1
%e A126743 0,0,0,0,0,6,5,1,1
%e A126743 0,0,0,0,0,0,0,73,76,80,25,15,15
%e A126743 0,0,0,0,0,0,0,0,0,1044,1475,2205,2643,983,1050,1208,958
%e A126743 0,0,0,0,0,0,0,0,0,0,0,15980,26548,48766,79579,99860,45898,60433,89890,109424,84312
%e A126743 0,0,0,0,0,0,0,0,0,0,0,0,0,245955,458397,948201,1857965,3160371,4153971,2217787,3402761,5855953,9067535,11402651,9170285
%e A126743 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3807508,7710844,17354771,37983463,...
%Y A126743 Row sums give A126742. Cf. A000105, A125759, A125761, A125709, A125753.
%K A126743 nonn,tabf
%O A126743 1,12
%A A126743 _David Applegate_ and _N. J. A. Sloane_, Feb 04 2007
%E A126743 Rows 5, 6, 7 and 8 from _David Applegate_, Feb 16 2007