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.

A087425 a(n) = S(5*n,5)/S(n,5) where S(n,m) = Sum_{k=0..n} binomial(n,k)*Fibonacci(m*k).

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%I A087425 #12 Jul 07 2021 07:20:14
%S A087425 23105,459119455,9758296035305,208416652653910655,
%T A087425 4452963734477926435505,95143212432467064852443605,
%U A087425 2032859482921447476046969568705,43434715031065603778576465510557055
%N A087425 a(n) = S(5*n,5)/S(n,5) where S(n,m) = Sum_{k=0..n} binomial(n,k)*Fibonacci(m*k).
%F A087425 a(n) = 121^n+{(21367+9555*sqrt(5))/2}^n+{(21367-9555*sqrt(5))/2}^n+{(1617+715*sqrt(5))/2}^n+{(1617-715*sqrt(5))/2}^n.
%F A087425 a(n) = (x_1)^n+(x_2)^n+(x_3)^n+(x_4)^n+(x_5)^n where (x_i) (1<=i<=5) are the roots of X^5-23105*X^4+37360785*X^3-4520654985*X^2+40931916905*X-25937424601.
%p A087425 S:=proc(n,m) add(binomial(n,k)*combinat:-fibonacci(m*k),k=0..n) end: m:=5: seq(S(m*n,m)/S(n,m),n=1..16); # _Georg Fischer_, Jul 07 2021
%Y A087425 Cf. A020876.
%Y A087425 Cf. A087423 (m=3), A087424 (m=4).
%K A087425 nonn
%O A087425 1,1
%A A087425 _Benoit Cloitre_, Oct 22 2003