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A308359 Triangle T(n,w) read by rows: the number of fixed polyominoes with n cells and width w of the convex hull. 2
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

The sequence counts the fixed n-ominoes with prescribed bounding box width w and variable height w<=h<=n.

LINKS

Table of n, a(n) for n=1..66.

FORMULA

T(n,1)=T(n,n)=1 (the straight n-ominoes).

Conjecture: T(n,n-1) = 4*n-8 for n>=3.

Conjecture: T(n,n-2)= 8*n^2-51*n+86 for n>=5.

EXAMPLE

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 2x2 box, 4 L-tetrominoes in a 3x2 box, 2 T-tetromoes in a 3x2 box, and 2 Z-tetrominoes in a 3x2 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 ;

CROSSREFS

Cf. A027053 (column w=2), A001168 (row sums), A273895.

Sequence in context: A110511 A082950 A060102 * A199065 A152237 A176282

Adjacent sequences:  A308356 A308357 A308358 * A308360 A308361 A308362

KEYWORD

nonn,tabl

AUTHOR

R. J. Mathar, May 22 2019

STATUS

approved

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Last modified August 24 02:32 EDT 2019. Contains 326260 sequences. (Running on oeis4.)