A059683 Triangle T(n,k) giving number of 3 X k polyominoes with n cells (n >= 3, 1<=k<=n-2).

1, 0, 3, 0, 2, 9, 0, 1, 12, 15, 0, 0, 12, 39, 25, 0, 0, 4, 59, 96, 35, 0, 0, 1, 42, 210, 188, 49, 0, 0, 0, 21, 255, 550, 332, 63, 0, 0, 0, 4, 212, 954, 1231, 529, 81, 0, 0, 0, 1, 103, 1184, 2800, 2406, 800, 99, 0, 0, 0, 0, 33, 964, 4634, 6818, 4313, 1142, 121, 0, 0, 0, 0, 6, 546, 5497, 14182, 14722, 7171, 1580

Offset

3,3

Comments

Note that for k=3 (polyominoes with square bounding rectangle) these are not the free polyominoes, because Read does not apply the full symmetry group of order 8 to reduce the fixed polyominoes for c_q(n), but only the symmetry group of order 4 (excluding the 90 deg rotations). The free polyominoes with square bounding rectangles are the z_3(n) instead. - R. J. Mathar, May 12 2019

Links

Table of n, a(n) for n=3..79.

R. C. Read, Contributions to the cell growth problem, Canad. J. Math., 14 (1962), 1-20.

Example

Triangle starts:
1;
0,3;
0,2,9;
0,1,12,15;
...

Crossrefs

Sequence in context: A354905 A099095 A061980 * A030208 A209939 A231101

Adjacent sequences: A059680 A059681 A059682 * A059684 A059685 A059686

Keyword

nonn,easy,nice,tabl

Author

N. J. A. Sloane, Feb 05 2001

Extensions

Values for n>=11 cells from R. J. Mathar, May 12 2019

Status

approved