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A177351 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. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
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.
LINKS
EXAMPLE
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;
MATHEMATICA
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[%]
CROSSREFS
Sequence in context: A225310 A131358 A291895 * A117901 A074984 A112658
KEYWORD
nonn,tabf
AUTHOR
Roger L. Bagula, Dec 10 2010
STATUS
approved

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Last modified April 12 11:25 EDT 2024. Contains 371634 sequences. (Running on oeis4.)