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A091594
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Triangle read by rows: T(n,m) := Sum_{k=0..floor((n-m)/2)} binomial(n-2k,m) * binomial(n-m-k,k).
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1
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1, 1, 1, 2, 2, 1, 3, 4, 3, 1, 5, 8, 7, 4, 1, 8, 15, 16, 11, 5, 1, 13, 28, 34, 28, 16, 6, 1, 21, 51, 70, 66, 45, 22, 7, 1, 34, 92, 140, 148, 116, 68, 29, 8, 1, 55, 164, 274, 320, 281, 190, 98, 37, 9, 1, 89, 290, 527, 672, 651, 494, 295, 136, 46, 10, 1, 144, 509, 999, 1379, 1456, 1219, 819, 439, 183, 56, 11, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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COMMENTS
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A Fibonacci related number triangle.
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LINKS
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FORMULA
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k-th column has g.f. 1/(1-x-x^2) * ( x*(1-x^2)/(1-x-x^2) )^k.
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EXAMPLE
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Rows begin:
1,
1, 1,
2, 2, 1,
3, 4, 3, 1,
5, 8, 7, 4, 1,
8, 15, 16, 11, 5, 1,
13, 28, 34, 28, 16, 6, 1,
21, 51, 70, 66, 45, 22, 7, 1,
...
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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