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A234713 Triangle, read by rows, based on the Fibonacci numbers. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified December 8 22:05 EST 2022. Contains 358698 sequences. (Running on oeis4.)