A125761 Triangle read by rows: T(n,k) (n>=1) gives the number of n-indecomposable polyominoes with k cells (k >= 1).

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

Offset

1,4

Comments

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.

Row n has 4n-3 nonzero terms.

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

Rows converge to A000105. - Andrey Zabolotskiy, Dec 26 2017

Links

Table of n, a(n) for n=1..110.

N. MacKinnon, Some thoughts on polyomino tilings, Math. Gaz., 74 (1990), 31-33.

Simone Rinaldi and D. G. Rogers, Indecomposability: polyominoes and polyomino tilings, The Mathematical Gazette 92.524 (2008): 193-204.

Example

Triangle begins:
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;
1,1,2,5,12,35,108,369,1285,1044,1475,2205,2643,983,1050,1208,958;
1,1,2,5,12,35,108,369,1285,4655,17073,15980,26548,48766,79579,99860,45898,60433,89890,109424,84312;
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,...

Crossrefs

Row sums give A125759.

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

Sequence in context: A093466 A257463 A293483 * A154950 A260089 A296240

Adjacent sequences: A125758 A125759 A125760 * A125762 A125763 A125764

Keyword

nonn,tabf

Author

David Applegate and N. J. A. Sloane, Feb 05 2007

Extensions

Rows 5, 6, 7 and 8 from David Applegate, Feb 16 2007

Status

approved