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A054447 Row sums of triangle A054446 (partial row sums triangle of Fibonacci convolution triangle). 3
1, 3, 9, 26, 73, 201, 545, 1460, 3873, 10191, 26633, 69198, 178889, 460437, 1180545, 3016552, 7684481, 19522203, 49473097, 125093506, 315654537, 795016545, 1998909985, 5017895196, 12578040097, 31485713511 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..25.

FORMULA

a(n) = Sum_{m=0..n} A054446(n,m) = ((n+1)*P(n+2)+(2-n)*P(n+1))/4, with P(n)=A000129(n) (Pell numbers).

G.f.: Pell(x)/(1-x*Fib(x)) = (Pell(x)^2)/Fib(x), 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).

a(n) = sum(k*sum(binomial(i,n-k-i)*binomial(k+i-1,k-1),i,ceiling((n-k)/2),n-k),k,1,n), n>0. - Vladimir Kruchinin, Sep 06 2010

a(n) = 4*a(n-1) - 2*a(n-2) - 4*a(n-3) - a(n-4), a(0)=1, a(1)=3, a(2)=9, a(3)=26. - Philippe Deléham, Jan 22 2014

PROG

(Maxima) a(n):=sum(k*sum(binomial(i, n-k-i)*binomial(k+i-1, k-1), i, ceiling((n-k)/2), n-k), k, 1, n); /* Vladimir Kruchinin, Sep 06 2010 */

CROSSREFS

Cf. A000129, A000045, A054446.

Sequence in context: A057153 A084787 A121190 * A061667 A234270 A258911

Adjacent sequences:  A054444 A054445 A054446 * A054448 A054449 A054450

KEYWORD

easy,nonn

AUTHOR

Wolfdieter Lang, Apr 27 2000

STATUS

approved

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Last modified January 22 10:32 EST 2019. Contains 319363 sequences. (Running on oeis4.)