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 A254884 #20 Aug 03 2015 12:42:09
%S A254884 0,-1,3,4,21,45,144,351,987,2516,6765,17533,46368,120927,317811,
%T A254884 830820,2178309,5699693,14930352,39079807,102334155,267892404,
%U A254884 701408733,1836254589,4807526976,12586118975,32951280099,86267178436,225851433717,591285701421,1548008755920
%N A254884 a(n) = Fibonacci(2*n) + ((-1)^n-1)*Fibonacci(n).
%H A254884 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3, 2, -9, 2, 3, -1).
%F A254884 Let phi = (1+sqrt(5))/2, p(n) = phi^n - (-phi)^(-n) and FL(n) = 1 + (p(n-1) + p(n+1) + p(2*n-1)) / sqrt(5).
%F A254884 a(n) = FL(-n) - FL(n). By this definition a(n) is a doubly infinite sequence.
%F A254884 a(n) = -a(-n) for all n in Z.
%F A254884 a(n) = A006172(n) - A005522(n).
%F A254884 a(2*n) = A033888(n).
%F A254884 G.f.: x/(x^2-3*x+1) + x/(x^2-x-1) + x/(x^2+x-1).
%F A254884 a(n) = 4*a(n-1) - a(n-2) - 11*a(n-3) + 11*a(n-4) + a(n-5) - 4*a(n-6) + a(n-7).
%p A254884 gf := x -> x/(x^2-3*x+1) + x/(x^2-x-1) + x/(x^2+x-1):
%p A254884 seq(coeff(series(gf(x),x,n+1),x,n), n=0..30);
%t A254884 LinearRecurrence[{4,-1,-11,11,1,-4,1}, {0,-1,3,4,21,45,144}, 31]
%t A254884 LinearRecurrence[{3, 2, -9, 2, 3, -1},{0, -1, 3, 4, 21, 45},31] (* _Ray Chandler_, Aug 03 2015 *)
%o A254884 (Sage)
%o A254884 A254884 = lambda n: fibonacci(2*n) + ((-1)^n-1)*fibonacci(n)
%o A254884 [A254884(n) for n in range(31)]
%Y A254884 Cf. A000032, A000045, A005522, A006172, A022112, A033888.
%K A254884 sign,easy
%O A254884 0,3
%A A254884 _Peter Luschny_, Mar 09 2015