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 A203169 #12 Jun 13 2015 00:54:08
%S A203169 0,1,82,4178,198659,9349284,439330980,20639983621,969645224182,
%T A203169 45552722051318,2140008541351943,100534850436141384,
%U A203169 4722997973709689160,221880369994471370761,10423654392318557192602,489689876072761951752602
%N A203169 Sum of the fourth powers of the first n even-indexed Fibonacci numbers.
%C A203169 Natural bilateral extension (brackets mark index 0): ..., -9349284, -198659, -4178, -82, -1, 0, [0], 1, 82, 4178, 198659, 9349284, ... That is, a(-n) = -a(n-1).
%H A203169 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (56,-440,770,-440,56,-1).
%F A203169 Let F(n) be the Fibonacci number A000045(n).
%F A203169 a(n) = sum_{k=1..n} F(2k)^4.
%F A203169 Closed form: a(n) = (1/75)(F(8n+4) - 12 F(4n+2) + 9(2 n + 1)).
%F A203169 Recurrence: a(n) - 56 a(n-1) + 440 a(n-2) - 770 a(n-3) + 440 a(n-4) - 56 a(n-5) + a(n-6) = 0.
%F A203169 G.f.: A(x) = (x + 26 x^2 + 26 x^3 + x^4)/(1 - 56 x + 440 x^2 - 770 x^3 + 440 x^4 - 56 x^5 + x^6) = x(1 + x)(1 + 25 x + x^2)/((1 - x)^2 (1 - 7 x + x^2)(1 - 47 x + x^2)).
%t A203169 a[n_Integer] := (1/75)(Fibonacci[8n+4] - 12*Fibonacci[4n+2] + 9*(2*n+1)); Table[a[n], {n, 0, 20}]
%Y A203169 Cf. A203170, A203171, A203172.
%Y A203169 Cf. A027941, A103434, A163198.
%K A203169 nonn,easy
%O A203169 0,3
%A A203169 _Stuart Clary_, Dec 30 2011