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A247704
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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 L; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
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5
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1, 1, 0, 3, 0, 2, 36, 16, 4, 0, 177, 220, 100, 0, 4, 1300, 1720, 816, 144, 26, 0, 8866, 11152, 5616, 1784, 524, 0, 8, 54849, 85016, 51116, 18380, 4656, 584, 88, 0, 372943, 622732, 448744, 189360, 52130, 8948, 1908, 0, 16, 2466986, 4528336, 3670116, 1806160, 582250, 127140, 22206, 1912, 248, 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) = A247737(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 : 36, 16, 4, 0;
04 : 177, 220, 100, 0, 4;
05 : 1300, 1720, 816, 144, 26, 0;
06 : 8866, 11152, 5616, 1784, 524, 0, 8;
07 : 54849, 85016, 51116, 18380, 4656, 584, 88, 0;
08 : 372943, 622732, 448744, 189360, 52130, 8948, 1908, 0, 16;
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CROSSREFS
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Row sums give A174249 or A233427(n,5).
Column k=0 gives A247768.
Cf. A247737.
Sequence in context: A350464 A247706 A361527 * A127802 A165951 A300288
Adjacent sequences: A247701 A247702 A247703 * A247705 A247706 A247707
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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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