%I #15 Dec 26 2017 16:07:30

%S 1,1,1,2,1,1,1,1,2,5,12,6,5,1,1,1,1,2,5,12,35,108,73,76,80,25,15,15,1,

%T 1,2,5,12,35,108,369,1285,1044,1475,2205,2643,983,1050,1208,958,1,1,2,

%U 5,12,35,108,369,1285,4655,17073,15980,26548,48766,79579,99860,45898,60433,89890,109424,84312,1,1,2,5,12,35,108,369,1285,4655,17073,63600,238591,245955,458397,948201,1857965,3160371,4153971,2217787,3402761,5855953,9067535,11402651,9170285,1,1,2,5,12,35,108,369,1285,4655,17073,63600,238591,901971,3426576,3807508,7710844,17354771,37983463

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

%C 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 Row n has 4n-3 nonzero terms.

%C For full lists of drawings of these polyominoes for n <= 6, see the links in A125759.

%C Rows converge to A000105. - _Andrey Zabolotskiy_, Dec 26 2017

%H N. MacKinnon, <a href="http://www.jstor.org/stable/3618845">Some thoughts on polyomino tilings</a>, Math. Gaz., 74 (1990), 31-33.

%H 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 Triangle begins:

%e 1;

%e 1,1,2,1,1;

%e 1,1,2,5,12,6,5,1,1;

%e 1,1,2,5,12,35,108,73,76,80,25,15,15;

%e 1,1,2,5,12,35,108,369,1285,1044,1475,2205,2643,983,1050,1208,958;

%e 1,1,2,5,12,35,108,369,1285,4655,17073,15980,26548,48766,79579,99860,45898,60433,89890,109424,84312;

%e 1,1,2,5,12,35,108,369,1285,4655,17073,63600,238591,245955,458397,948201,1857965,3160371,4153971,2217787,3402761,5855953,9067535,11402651,9170285;

%e 1,1,2,5,12,35,108,369,1285,4655,17073,63600,238591,901971,3426576,3807508,7710844,17354771,37983463,...

%Y Row sums give A125759.

%Y Cf. A125709, A125753, A126742, A126743; A000105, A195738, A195739, A049430.

%K nonn,tabf

%O 1,4

%A _David Applegate_ and _N. J. A. Sloane_, Feb 05 2007

%E Rows 5, 6, 7 and 8 from _David Applegate_, Feb 16 2007