A308359 Triangle T(n,w) read by rows: the number of fixed polyominoes with n cells and width w of the convex hull.
1, 1, 1, 1, 4, 1, 1, 9, 8, 1, 1, 18, 31, 12, 1, 1, 35, 95, 68, 16, 1, 1, 66, 269, 282, 121, 20, 1, 1, 123, 721, 1027, 638, 190, 24, 1, 1, 228, 1866, 3468, 2817, 1226, 275, 28, 1, 1, 421, 4728, 11132, 11254, 6391, 2110, 376, 32, 1, 1, 776, 11804, 34558, 42099, 29388, 12758, 3354, 493, 36, 1
Offset: 1
Examples
T(3,2) = 4 counts the 4 variants of the L-shaped tromino rotated by multiples of 90 degrees. T(4,2) = 9 counts one O-tetromino in a 2 X 2 box, 4 L-tetrominoes in a 3 X 2 box, 2 T-tetromoes in a 3 X 2 box, and 2 Z-tetrominoes in a 3 X 2 box. The triangle starts 1; 1, 1; 1, 4, 1; 1, 9, 8, 1; 1, 18, 31, 12, 1; 1, 35, 95, 68, 16, 1; 1, 66, 269, 282, 121, 20, 1;
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Crossrefs
Formula
T(n,1) = T(n,n) = 1 (the straight n-ominoes).
T(n,n-1) = 4*n-8 for n >= 3 (width n-1 and height 2).
Conjecture: T(n,n-2) = 8*n^2 - 51*n + 86 for n >= 5.
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