A335711 -id:A335711 - cp's OEIS frontend

A268371 Triangle read by rows: T(n,k) is the number of free polyominoes with width n and height 1<=k<=n.

1, 1, 2, 1, 6, 24, 1, 12, 181, 1051, 1, 30, 941, 21992, 238048, 1, 65, 4662, 228013, 9735647, 195284973, 1, 158, 23691, 2337694, 195616247, 15256715219, 577169894573

Offset: 1

John Mason, Feb 03 2016

Superset of Craig Knecht's A268311.

			The first rows of the array are:
1;
1, 2;
1, 6, 24;
1, 12, 181, 1051;
...
T(4,3)=181 = 15+39+59+42+21+4+1: In the 4x3 square fit 15 6-ominoes, 39 7-ominoes, 59 8-ominoes, 42 9-ominoes, 21 10-ominoes, 4 11-ominoes or 1 12-omino. - _R. J. Mathar_, Jun 07 2020

Jean-Luc Manguin, Table of n, a(n) for n = 1..28
R. J. Mathar, Corrigendum to "Polyomino Enumeration Results (Parkin et al, SIAM Fall Meeting 1967)" viXra:1905.0474 (2019)
R. Parkin, L. J. Lander, and D. R. Parkin, Polyomino Enumeration Results, presented at SIAM Fall Meeting, 1967, and accompanying letter from T. J. Lander (annotated scanned copy) page 9 (incorrect at n=15).
Index entries for sequences related to polyominoes

Cf. A268311 (right diagonal), A335711 (column n=2), A000105 (free polyominoes), A292357 (equival. for fixed polys).

a(16)-a(28) from Jean-Luc Manguin, May 25 2020

A352720 a(n) is the number of free polyominoes of width 2 and size n.

Original entry on oeis.org

1, 1, 4, 5, 12, 18, 37, 60, 117, 200, 379, 669, 1250, 2247, 4168, 7570, 13987, 25549, 47108, 86319, 158978, 291806, 537105, 986786, 1815699, 3337560, 6140047, 11289571, 20767180, 38189927, 70246680, 129191148, 237627757, 437042337, 803861244, 1478488577, 2719392160, 5001663330, 9199544069

Offset: 2

John Mason, Mar 31 2022

nonn

			There is one polyomino, the domino, of width 2 and size 2. So a(2) = 1.
There is one tromino, L-shaped, of width 2. So a(3) = 1.

John Mason, Table of n, a(n) for n = 2..1000
John Mason, Java program
John Mason, Explanation of formulas
R. J. Mathar, Corrigendum to "polyomino enumeration results" (Parkin et al), vixra:1905.0474 (2019) Table 1 column 2.

Cf. A000105, A335711, A353067.

For a set of recursive formulas to generate a(n), see the link for the Java program extract.

A336267 Number of free polyominoes of width 3 and height n.

Original entry on oeis.org

1, 6, 24, 181, 941, 4662, 23691, 119271, 603760, 3050402, 15428576, 78004550, 394462578, 1994595585, 10086050889, 51001111356, 257894037378, 1304071170194, 6594196094078, 33344335235915, 168609627579175, 852594638783225, 4311246376730011

Offset: 1

Jean-Luc Manguin, Jul 15 2020

nonn

The sequence can be generated using a series of recursive formulas in a fashion similar to A353067. - John Mason, Nov 04 2022

			a(2)=6, bounding box 2 X 3 as in A335711.

John Mason, Table of n, a(n) for n = 1..400

Cf. A268371, A335711, A353067.

More terms from John Mason, Nov 04 2022

cp's OEIS Frontend

A268371 Triangle read by rows: T(n,k) is the number of free polyominoes with width n and height 1<=k<=n.

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A352720 a(n) is the number of free polyominoes of width 2 and size n.

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A336267 Number of free polyominoes of width 3 and height n.

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