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

Author

Roger L. Bagula, Dec 10 2010

Keywords

• nonn
• tabf

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.

Examples

			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;
		

Crossrefs

Cf. A000045

Programs

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[%]