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A177351
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Triangle t(n,k)= sum_{m=1..floor(n/2-k)} binomial(n-m-k,m+k), -floor(n/2) <= k <= floor(n/2), read by rows.
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1
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0, 0, 2, 1, 0, 3, 2, 0, 5, 5, 4, 1, 0, 8, 8, 7, 3, 0, 13, 13, 13, 12, 7, 1, 0, 21, 21, 21, 20, 14, 4, 0, 34, 34, 34, 34, 33, 26, 11, 1, 0, 55, 55, 55, 55, 54, 46, 25, 5, 0, 89, 89, 89, 89, 89, 88, 79, 51, 16, 1, 0
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OFFSET
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0,3
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COMMENTS
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Row sums are 0, 0, 3, 5, 15, 26, 59, 101, 207, 350, 680,...
The first column is essentially A000045, and the other columns also join the Fibonacci sequence after some transient initial terms.
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LINKS
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Table of n, a(n) for n=0..60.
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EXAMPLE
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0;
0;
2, 1, 0;
3, 2, 0;
5, 5, 4, 1, 0;
8, 8, 7, 3, 0;
13, 13, 13, 12, 7, 1, 0;
21, 21, 21, 20, 14, 4, 0;
34, 34, 34, 34, 33, 26, 11, 1, 0;
55, 55, 55, 55, 54, 46, 25, 5, 0;
89, 89, 89, 89, 89, 88, 79, 51, 16, 1, 0;
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MATHEMATICA
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w[n_, m_, k_] = Binomial[n - (m + k), m + k];
t[n_, k_] := Sum[w[n, m, k], {m, 1, Floor[n/2 - k]}];
Table[Table[t[n, k], {k, -Floor[n/2], Floor[n/2]}], {n, 0, 10}];
Flatten[%]
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CROSSREFS
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Cf. A000045
Sequence in context: A225310 A131358 A291895 * A117901 A074984 A112658
Adjacent sequences: A177348 A177349 A177350 * A177352 A177353 A177354
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KEYWORD
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nonn,tabf
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AUTHOR
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Roger L. Bagula, Dec 10 2010
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STATUS
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approved
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