%I A014334
%S A014334 0,0,2,6,22,70,230,742,2406,7782,25190,81510,263782,853606,
%T A014334 2762342,8939110,28927590,93611622,302933606,980313702,
%U A014334 3172361830,10265978470,33221404262,107506722406,347899061862
%N A014334 Exponential convolution of Fibonacci numbers with themselves.
%F A014334 a(0)=0, a(1)=0, a(2)=2, a(n)=3a(n-1)+2a(n-2)-4a(n-3); n>0, a(n)=sum(k=0, 
               n-1, 2^k*F(k)) where F(k) is the k-th Fibonacci number; a(n)=-2/5+((1+sqrt(5))^n+(1-sqrt(5))^n)/
               5 - Benoit Cloitre (benoit7848c(AT)orange.fr), May 29 2003
%F A014334 a(n)=sum(k=0, n, F(k)*F(n-k)*binomial(n, k)) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               May 11 2005
%o A014334 (PARI) a(n)=if(n<1,0,sum(k=0,n-1,fibonacci(k)*2^k))
%Y A014334 Cf. A000045.
%Y A014334 Cf. A103435.
%Y A014334 Sequence in context: A126171 A002839 A109194 this_sequence A107239 A148496 
               A106434
%Y A014334 Adjacent sequences: A014331 A014332 A014333 this_sequence A014335 A014336 
               A014337
%K A014334 nonn
%O A014334 0,3
%A A014334 N. J. A. Sloane (njas(AT)research.att.com).