A087603 - OEIS

%I #13 Mar 30 2016 14:19:05

%S 1,10,155,2100,29525,410750,5731375,79905000,1114275625,15537531250,

%T 216660471875,3021168937500,42128015328125,587444444843750,

%U 8191485291484375,114224297381250000,1592774664844140625,22210083004410156250,309703436610529296875

%N a(n) = (1/8)*Sum_{k=0..n} binomial(n,k)*Fibonacci(k)*8^k.

%C More generally a(n)=(1/x)*sum(k=0,n,binomial(n,k)*Fibonacci(k)*x^k) satisfies the recurrence formula a(n)=(x+2)*a(n-1)+(x^2-x-1)*a(n-2).

%H Harvey P. Dale, <a href="/A087603/b087603.txt">Table of n, a(n) for n = 0..873</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10, 55).

%F a(n) = 10*a(n-1)+55*a(n-2).

%F G.f.: -1/(-1+10*x+55*x^2). - _R. J. Mathar_, Dec 05 2007

%F a(n) = ((-(5-4*sqrt(5))^(1+n)+(5+4*sqrt(5))^(1+n)))/(8*sqrt(5)). - _Colin Barker_, Mar 30 2016

%t LinearRecurrence[{10,55},{1,10},30] (* _Harvey P. Dale_, Nov 26 2014 *)

%o (PARI) Vec(1/(1-10*x-55*x^2) + O(x^50)) \\ _Colin Barker_, Mar 30 2016

%Y Cf. A014445, A057088, A015553.

%K nonn,easy

%O 0,2

%A _Benoit Cloitre_, Oct 25 2003