

A059684


Triangle T(n,k) giving number of 4 X k polyominoes with n cells (n >= 4, 1<=k<=n3).


2



1, 0, 3, 0, 6, 15, 0, 2, 39, 30, 0, 1, 59, 148, 61, 0, 0, 42, 349, 383, 97, 0, 0, 21, 519, 1304, 822, 155, 0, 0, 4, 488, 2847, 3548, 1551, 220, 0, 0, 1, 321, 4441, 10323, 8239, 2680, 313, 0, 0, 0, 122, 5008, 21995, 29442, 16821, 4327, 415, 0, 0, 0, 35, 4168, 36035, 79155, 71742, 31576
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OFFSET

4,3


COMMENTS

Note that for k=4 (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 d_q(n), but only the symmetry group of order 4 (excluding the 90 deg rotations). The free polyominoes with square bounding rectangles are his z_4(n) instead.  R. J. Mathar, May 12 2019


LINKS



EXAMPLE

Triangle starts:
1;
0,3;
0,6,15;
0,2,39, 30;
0,1,59,148, 61;
0,0,42,349, 383, 97;
0,0,21,519,1304, 822, 155;
0,0, 4,488,2847, 3548, 1551, 220;
0,0, 1,321,4441,10323, 8239, 2680, 313;
0,0, 0,122,5008,21995,29442,16821, 4327,415;
0,0, 0, 35,4168,36035,79155,71742,31576,...
There are T(5,2)=3 out of 12 pentominoes that fill the 4X2 shape: the L, N and Y. The F, T, V, W, X, and Z require both dimensions >= 3; the P and U would fit but not touch all sides; the I requires one dimension of 5.  R. J. Mathar, May 08 2019


CROSSREFS

Cf. A059680 (flipped or rotated considered distinct).


KEYWORD



AUTHOR



EXTENSIONS

Changed 518 to 519 (correcting Read...) and added values for n>=11 cells. R. J. Mathar, May 12 2019


STATUS

approved



