A234713 Triangle, read by rows, based on the Fibonacci numbers.

0, 1, 1, 1, 3, 2, 2, 6, 7, 3, 3, 13, 20, 14, 4, 5, 25, 51, 51, 25, 5, 8, 48, 118, 154, 111, 41, 6, 13, 89, 260, 416, 393, 217, 63, 7, 21, 163, 548, 1042, 1218, 890, 392, 92, 8, 34, 294, 1121, 2465, 3435, 3127, 1842, 666, 129, 9, 55, 525, 2236, 5586, 9035, 9845

Offset

0,5

Comments

First column is the Fibonacci sequence.

Sum_{k=0..n} T(n,k)*2^k = -A106732(n).

Links

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

Formula

G.f.: (y+1)*x/(1-(2y+1)*x+(y^2-1)*x^2).

T(n,k)=T(n-1,k)+2*T(n-1,k-1)+T(n-2,k)-T(n-2,k-2), T(0,0)=0, T(1,0)=1, T(1,1)=1, T(n,k)=0 if k<0 or if k>n.

Example

Triangle begins:
0
1, 1
1, 3, 2
2, 6, 7, 3
3, 13, 20, 14, 4
5, 25, 51, 51, 25, 5
8, 48, 118, 154, 111, 41, 6
13, 89, 260, 416, 393, 217, 63, 7
21, 163, 548, 1042, 1218, 890, 392, 92, 8

Crossrefs

Cf. Diagonals: A001477, A004006.

Cf. Columns: A000045 (Fibonacci), A131913, A261054.

Cf. A025192 (row sums for n>0), A006054 (diagonal sums)

Sequence in context: A111702 A283557 A283558 * A091029 A272372 A354002

Adjacent sequences: A234710 A234711 A234712 * A234714 A234715 A234716

Keyword

nonn,easy,tabl

Author

Philippe Deléham, Dec 29 2013

Status

approved