A121194
Number of n-celled polyominoes, where the cells are 1 X 2 rectangles with one edge of length 2 replaced by a curved arc that either sags inwards or bulges outwards, subject to some restrictions.
Original entry on oeis.org
A213377
Number of polyominoes of order 2n that can be tiled by dominoes in a unique way.
Original entry on oeis.org
1, 3, 20, 170, 1728, 18878, 214278, 2488176, 29356463
Offset: 1
A213378
Number of polyominoes of order 2n that can be tiled by dominoes in more than one way.
Original entry on oeis.org
0, 1, 3, 41, 499, 6946, 95964, 1330807, 18395673
Offset: 1
A056845
Number of distinct connected planar figures that can be formed from n non-overlapping diamonds.
Original entry on oeis.org
1, 2, 9, 41, 248, 1610, 11065, 78218, 563675, 4113988, 30329616, 225394071, 1686227909
Offset: 1
Title clarified, a(6) corrected and a(7)-a(13) from
Aaron N. Siegel, May 18 2022
A308437
Triangle read by rows: T(n,k) = number of ways, summed over the free n-ominoes, that an n-omino with an assigned orientation can be maximally (partially) covered by k X 1 tiles.
Original entry on oeis.org
1, 1, 1, 2, 4, 1, 5, 8, 4, 1, 12, 35, 18, 4, 1, 35, 89, 61, 22, 5, 1, 108, 425, 206, 97, 28, 5, 1, 369, 1438, 739, 436, 141, 36, 6, 1, 1285, 6818, 3008, 1853, 687, 193, 44, 6, 1, 4655, 27713, 12823, 7668, 3233, 1039, 268, 54, 7, 1, 17073, 125830, 51619, 30902, 14731, 5164, 1518, 351, 64, 7, 1
Offset: 1
The triangle starts with n >= 1, 1 <= k <= n as follows:
1;
1, 1;
2, 4, 1;
5, 8, 4, 1;
12, 35, 18, 4, 1;
35, 89, 61, 22, 5, 1;
108, 425, 206, 97, 28, 5, 1;
369, 1438, 739, 436, 141, 36, 6, 1;
1285, 6818, 3008, 1853, 687, 193, 44, 6, 1;
(...)
From _M. F. Hasler_ and _R. J. Mathar_, May 27 2019: (Start)
We have T(n,1) = A000105(n) which is the number of different inequivalent n-ominoes, and each one can be maximally filled in exactly one (trivial) way with 1 X 1 monominoes.
We have T(n,n) = 1 because only the straight n X 1 polyomino can be filled in the required way, namely with only straight n-ominoes.
T(3,2) = 4 counts 2 ways of placing a domino into the straight tromino (the two ends of the tromino considered distinct) and 2 ways of placing a domino into the L-tromino (again the two variants obtained by flipping along the diagonal considered distinct). (End)
Comments