A126743 - OEIS

%I #9 Jan 23 2019 20:01:13

%S 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 0,0,0,0,0,0,1044,1475,2205,2643,983,1050,1208,958,0,0,0,0,0,0,0,0,0,

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

%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 terms of which the first 2n-1 are zero.

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

%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 0

%e 0,0,0,1,1

%e 0,0,0,0,0,6,5,1,1

%e 0,0,0,0,0,0,0,73,76,80,25,15,15

%e 0,0,0,0,0,0,0,0,0,1044,1475,2205,2643,983,1050,1208,958

%e 0,0,0,0,0,0,0,0,0,0,0,15980,26548,48766,79579,99860,45898,60433,89890,109424,84312

%e 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 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3807508,7710844,17354771,37983463,...

%Y Row sums give A126742. Cf. A000105, A125759, A125761, A125709, A125753.

%K nonn,tabf

%O 1,12

%A _David Applegate_ and _N. J. A. Sloane_, Feb 04 2007

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