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.

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

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

Table of n, a(n) for n=0..60.

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

Cf. A000045

Sequence in context: A225310 A131358 A291895 * A117901 A074984 A112658

Adjacent sequences: A177348 A177349 A177350 * A177352 A177353 A177354

Keyword

nonn,tabf

Author

Roger L. Bagula, Dec 10 2010

Status

approved