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Triangle, read by rows, based on the Fibonacci numbers.
1

%I #6 Aug 08 2015 10:25:59

%S 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,

%T 6,13,89,260,416,393,217,63,7,21,163,548,1042,1218,890,392,92,8,34,

%U 294,1121,2465,3435,3127,1842,666,129,9,55,525,2236,5586,9035,9845

%N Triangle, read by rows, based on the Fibonacci numbers.

%C First column is the Fibonacci sequence.

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

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

%F 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.

%e Triangle begins:

%e 0

%e 1, 1

%e 1, 3, 2

%e 2, 6, 7, 3

%e 3, 13, 20, 14, 4

%e 5, 25, 51, 51, 25, 5

%e 8, 48, 118, 154, 111, 41, 6

%e 13, 89, 260, 416, 393, 217, 63, 7

%e 21, 163, 548, 1042, 1218, 890, 392, 92, 8

%Y Cf. Diagonals: A001477, A004006.

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

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

%K nonn,easy,tabl

%O 0,5

%A _Philippe Deléham_, Dec 29 2013