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Row sums of triangle A054448 (second member of partial row sums triangle family of Fibonacci convolution triangle).
1

%I #4 Mar 31 2012 13:20:01

%S 1,4,14,46,144,436,1287,3724,10603,29788,82748,227658,621122,1682252,

%T 4526845,12111512,32237253,85407188,225318042,592141478,1550688932,

%U 4047787844,10534503523,27340763556,70777265551,182785072876

%N Row sums of triangle A054448 (second member of partial row sums triangle family of Fibonacci convolution triangle).

%F a(n)= sum(A054448(n, m), m=0..n)= ((2*n^2+17*n+32)*P(n+1)+13*(n+1)*P(n))/32, P(n)= A000129(n) (Pell numbers).

%F G.f.: ((Pell(x))^3)/(Fib(x))^2, with Pell(x)= 1/(1-2*x-x^2) = g.f. A000129(n+1) (Pell numbers without 0) and Fib(x)=1/(1-x-x^2) = g.f. A000045(n+1) (Fibonacci numbers without 0).

%Y Cf. A000129, A000045, A054448.

%K easy,nonn

%O 0,2

%A _Wolfdieter Lang_, Apr 27 2000