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A247706
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Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape P; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
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6
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1, 1, 0, 3, 0, 2, 16, 20, 20, 0, 135, 204, 140, 16, 6, 944, 1432, 1164, 296, 170, 0, 4814, 8796, 8452, 4068, 1708, 92, 20, 26435, 58656, 66994, 41648, 17494, 2700, 762, 0, 158761, 410000, 520728, 371456, 175810, 46648, 12876, 440, 62, 978044, 2783560, 3836254, 3107308, 1696312, 609772, 172724, 18220, 3160, 0
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OFFSET
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0,4
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COMMENTS
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Sum_{k>0} k * T(n,k) = A247739(n).
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LINKS
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Alois P. Heinz, Rows n = 0..140, flattened
Wikipedia, Pentomino
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EXAMPLE
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T(2,2) = 2:
.___. .___.
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|___| |___| .
Triangle T(n,k) begins:
00 : 1;
01 : 1, 0;
02 : 3, 0, 2;
03 : 16, 20, 20, 0;
04 : 135, 204, 140, 16, 6;
05 : 944, 1432, 1164, 296, 170, 0;
06 : 4814, 8796, 8452, 4068, 1708, 92, 20;
07 : 26435, 58656, 66994, 41648, 17494, 2700, 762, 0;
08 : 158761, 410000, 520728, 371456, 175810, 46648, 12876, 440, 62;
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CROSSREFS
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Row sums give A174249 or A233427(n,5).
Column k=0 gives A247770.
Even bisection of main diagonal gives A247076.
Cf. A247739.
Sequence in context: A303102 A302953 A350464 * A361527 A247704 A127802
Adjacent sequences: A247703 A247704 A247705 * A247707 A247708 A247709
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KEYWORD
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nonn,tabl
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AUTHOR
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Alois P. Heinz, Sep 22 2014
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STATUS
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approved
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