A126743 - OEIS

A126743

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

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

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OFFSET

1,12

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

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

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:

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

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

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

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,...

CROSSREFS

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

Sequence in context: A278760 A199724 A373019 * A046613 A372777 A296470

Adjacent sequences: A126740 A126741 A126742 * A126744 A126745 A126746

KEYWORD

nonn,tabf

AUTHOR

David Applegate and N. J. A. Sloane, Feb 04 2007

EXTENSIONS

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

STATUS

approved