cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A087603 a(n) = (1/8)*Sum_{k=0..n} binomial(n,k)*Fibonacci(k)*8^k.

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%I A087603 #13 Mar 30 2016 14:19:05
%S A087603 1,10,155,2100,29525,410750,5731375,79905000,1114275625,15537531250,
%T A087603 216660471875,3021168937500,42128015328125,587444444843750,
%U A087603 8191485291484375,114224297381250000,1592774664844140625,22210083004410156250,309703436610529296875
%N A087603 a(n) = (1/8)*Sum_{k=0..n} binomial(n,k)*Fibonacci(k)*8^k.
%C A087603 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 A087603 Harvey P. Dale, <a href="/A087603/b087603.txt">Table of n, a(n) for n = 0..873</a>
%H A087603 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10, 55).
%F A087603 a(n) = 10*a(n-1)+55*a(n-2).
%F A087603 G.f.: -1/(-1+10*x+55*x^2). - _R. J. Mathar_, Dec 05 2007
%F A087603 a(n) = ((-(5-4*sqrt(5))^(1+n)+(5+4*sqrt(5))^(1+n)))/(8*sqrt(5)). - _Colin Barker_, Mar 30 2016
%t A087603 LinearRecurrence[{10,55},{1,10},30] (* _Harvey P. Dale_, Nov 26 2014 *)
%o A087603 (PARI) Vec(1/(1-10*x-55*x^2) + O(x^50)) \\ _Colin Barker_, Mar 30 2016
%Y A087603 Cf. A014445, A057088, A015553.
%K A087603 nonn,easy
%O A087603 0,2
%A A087603 _Benoit Cloitre_, Oct 25 2003