Search: id:A081057
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%I A081057
%S A081057 1,2,6,18,58,186,602,1946,6298,20378,65946,213402,690586,2234778,
%T A081057 7231898,23402906,75733402,245078426,793090458,2566494618,8305351066,
%U A081057 26876680602,86974765466,281456253338,910811568538,2947448150426
%N A081057 E.g.f.: sum(n>=0, a(n)*x^n/n!) = {sum(n>=0, F(n+1)*x^n/n!)}^2, where 
               F(n) is the n-th Fibonacci number.
%C A081057 a(n) ~ c*(sqrt(5)+1)^n, where c=(sqrt(5)+3)/10.
%F A081057 G.f.: (1-x-2x^2)/(1-3x-2x^2+4x^3). - Michael Somos, Mar 04 2003
%F A081057 a(n) - 2*a(n-1) = A014334(n), n>0. - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Mar 05 2003
%F A081057 a(n) = 2/5+(3/10-1/10*5^(1/2))*(1-5^(1/2))^n+(3/10+1/10*5^(1/2))*(1+5^(1/
               2))^n. Recurrence: a(n) = 3*a(n-1)+2*a(n-2)-4*a(n-3). G.f.: (1+x)*(1-2*x)/
               (1-2*x-4*x^2)/(1-x). - Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 
               05 2003
%Y A081057 a(n) = A052899(n-1) + A052899(n). a(n) - 2*a(n-1) = A014334(n).
%Y A081057 Sequence in context: A125305 A148458 A148459 this_sequence A000137 A151282 
               A157004
%Y A081057 Adjacent sequences: A081054 A081055 A081056 this_sequence A081058 A081059 
               A081060
%K A081057 nonn
%O A081057 0,2
%A A081057 Paul D. Hanna (pauldhanna(AT)juno.com), Mar 03 2003
%E A081057 Corrected and extended by Vladeta Jovovic (vladeta(AT)eunet.rs) and Michael 
               Somos, Mar 05 2003

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