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.
%I A201207 #17 Oct 24 2024 04:03:07
%S A201207 4,2,7,11,27,41,84,137,270,435,826,1338,2488,4024,7353,11899,21461,
%T A201207 34723,61960,100255,177344,286947,503892,815316,1422892,2302286,
%U A201207 3996619,6466667,11173935,18079805,31114236
%N A201207 Half-convolution of sequence A000032 (Lucas) with itself.
%C A201207 For the definition of the half-convolution of a sequence with itself see a comment on A201204. There the rule for the o.g.f. is given. Here the o.g.f. is (L(x)^2 + L2(x^2))/2, with the o.g.f. L(x)=(2-x)/(1-x-x^2) of A000032, and L2(x) = (4-7*x-x^2)/((1+x)*(1-3*x+x^2)) the o.g.f. of A001254. This leads to the o.g.f given in the formula section.
%C A201207 For the bisection of this sequence see A203570 and A203574.
%F A201207 a(n) = Sum_{k=0..floor(n/2)} L(k)*L(n-k), n >= 0, with the Lucas numbers L(n)=A000032(n).
%F A201207 O.g.f.: (4-2*x-7*x^2+6*x^3-x^4+3*x^5)/((1-3*x^2+x^4)*(1+x^2)*(1-x-x^2)). See a comment above.
%F A201207 a(n) = (1/4)*(2*(2*n+5+(-1)^n)*F(n+1)-(2*n+3+(-1)^n)*F(n)) +(i^n+(-i)^n)/2, n >= 0, with the Fibonacci numbers F(n)=A000045(n) and the imaginary unit i=sqrt(-1). From the partial fraction decomposition of the o.g.f. and the Fibonacci recurrence.
%Y A201207 Cf. A000032, A000045, A201204, A203570, A203574.
%K A201207 nonn,easy
%O A201207 0,1
%A A201207 _Wolfdieter Lang_, Jan 03 2012