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.

A279277 Composition of Lucas numbers A000032 with Fibonacci numbers A000045.

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%I A279277 #22 Dec 15 2016 11:17:39
%S A279277 1,4,12,37,110,327,968,2864,8469,25040,74029,218856,647008,1912753,
%T A279277 5654670,16716883,49420052,146100276,431915561,1276869920,3774804441,
%U A279277 11159436284,32990587972,97529916957,288327225550,852380393407,2519888066928,7449533000584,22023018662909
%N A279277 Composition of Lucas numbers A000032 with Fibonacci numbers A000045.
%C A279277 G(F(x)) where F(x) = x+x^2+2x^3+3x^4+... is the generating series of the Fibonacci numbers A000045 and G(x) = x+3x^2+4x^3+7x^4 +... is the generating series of the Lucas numbers A000032.
%H A279277 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,1,-3,-1).
%F A279277 G.f. x*(1+x-x^2)/(1-3*x-x^2+3*x^3+x^4).
%F A279277 a(n) = 3*a(n-1)+a(n-2)-3*a(n-3)-a(n-4), a(1)=1, a(2)=4, a(3)=12, a(4)=46.
%e A279277 (x+x^2)/(1-3x) = x + (3+1)x^2+... so a(1) = 1 and a(2) = 4.
%t A279277 Rest@ CoefficientList[Series[(x + x^2 - x^3)/(1 - 3 x - x^2 + 3 x^3 + x^4), {x, 0, 24}], x] (* _Michael De Vlieger_, Dec 12 2016 *)
%Y A279277 Cf. A000045, A000032, A270863.
%K A279277 nonn,easy
%O A279277 1,2
%A A279277 _Oboifeng Dira_, Dec 10 2016