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 A203570 #10 Mar 30 2012 18:49:34 %S A203570 4,7,27,84,270,826,2488,7353,21461,61960,177344,503892,1422892, %T A203570 3996619,11173935,31114236,86328978,238764238,658478176,1811322045, %U A203570 4970928809,13613135152,37208048132,101518052904,276527670100,752102592271 %N A203570 Bisection of A201207 (half-convolution of the Lucas sequence A000032 with itself); even part. %C A203570 The odd part of the bisection of A201207 is given in A203574. %C A203570 See a comment on A201204 for the definition of the half-convolution of a sequence with itself, and the rule for the o.g.f.s of the bisection. Here the o.g.f. is (Lconve(x) + L2(x))/2, with the o.g.f. Lconve(x) = (4-11*x+11*x^2+x^3)/ %C A203570 (1-3*x+x^2)^2 of A203573 and the o.g.f. L2(x)= (4-7*x-x^2)/ ((1+x)*(1-3*x+x^2)) of A001254. This leads to the o.g.f. given in the formula section. %F A203570 a(n) = A201207(2*n), n>=0. %F A203570 a(n) = (2*(4*n+6)*F(2*n+1)-4*(n+1)*F(2*n))/4 + (-1)^n, with the Fibonacci numbers F(n)=A000045(n). %F A203570 O.g.f.: (4-13*x+4*x^3+12*x^2)/((1-3*x+x^2)^2*(1+x)). See a comment above. %Y A203570 Cf. A201207, A203574. %K A203570 nonn %O A203570 0,1 %A A203570 _Wolfdieter Lang_, Jan 03 2012