

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
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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^21)*x^2).
T(n,k)=T(n1,k)+2*T(n1,k1)+T(n2,k)T(n2,k2), 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



