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 A163199 #10 Dec 10 2016 03:23:34
%S A163199 -1,0,27,539,9800,176175,3162159,56744792,1018249595,18271762299,
%T A163199 327873509424,5883451505855,105574253853887,1894453118539344,
%U A163199 33994581881622075,610008020755286075,10946149791725643704,196420688230338021807,3524626238354441796015,63246851602149831726824
%N A163199 Sum of the cubes of the first n even-indexed Fibonacci numbers, minus 1.
%C A163199 Natural bilateral extension (brackets mark index 0): ..., 9800, 539, 27, 0, -1, [-1], 0, 27, 539, 9800, 176175, ... This is A163199-reversed followed by A163199. That is, A163199(-n) = A163199(n-1).
%H A163199 G. C. Greubel, <a href="/A163199/b163199.txt">Table of n, a(n) for n = 0..500</a>
%H A163199 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (22,-77,77,-22,1).
%F A163199 Let F(n) be the Fibonacci number A000045(n) and let L(n) be the Lucas number A000032(n).
%F A163199 a(n) = Sum_{k=1..n} F(2k)^3 - 1.
%F A163199 a(n) = Sum_{k=2..n} F(2k)^3 for n > 0.
%F A163199 a(n) = A163198(n) - 1.
%F A163199 a(n) = (1/20)*(F(6n+3) - 12*F(2n+1) - 10).
%F A163199 a(n) = (1/4)*(F(2n+1)^3 - 3*F(2n+1) - 2).
%F A163199 a(n) = (1/4)*L(n)^2*F(n+1)^2*L(n-1)*F(n+2) = A163197(n) if n is even.
%F A163199 a(n) = (1/4)*F(n)^2*L(n+1)^2*F(n-1)*L(n+2) = A163195(n) if n is odd.
%F A163199 a(n) - 21 a(n-1) + 56 a(n-2) - 21 a(n-3) + a(n-4) = -8.
%F A163199 a(n) - 22 a(n-1) + 77 a(n-2) - 77 a(n-3) + 22 a(n-4) - a(n-5) = 0.
%F A163199 G.f.: (-1 + 22*x - 50*x^2 + 22*x^3 - x^4)/(1 - 22*x + 77*x^2 - 77*x^3 + 22*x^4 - x^5) = -(1 - 22*x + 50*x^2 - 22*x^3 + x^4)/((1 - x)*(1 - 3*x + x^2 )*(1 - 18*x + x^2)).
%t A163199 a[n_Integer] := If[ n >= 0, Sum[ Fibonacci[2k]^3, {k, 1, n} ] - 1, -Sum[ Fibonacci[-2k]^3, {k, 1, -n - 1} ] - 1 ]
%t A163199 Accumulate[Fibonacci[Range[0,40,2]]^3]-1 (* _Harvey P. Dale_, Jan 03 2016 *)
%t A163199 LinearRecurrence[{22,-77,77,-22,1},{-1,0,27,539,9800},50] (* or *) Table[(1/20)*(F(6n+3) - 12*F(2n+1) - 10),{n,0,25}] (* _G. C. Greubel_, Dec 09 2016 *)
%o A163199 (PARI) Vec(-(1 - 22*x + 50*x^2 - 22*x^3 + x^4)/((1 - x)*(1 - 3*x + x^2 )*(1 - 18*x + x^2)) + O(x^50)) \\ _G. C. Greubel_, Dec 09 2016
%Y A163199 Cf. A163194, A163195, A163196, A163197, A163198.
%K A163199 sign,easy
%O A163199 0,3
%A A163199 _Stuart Clary_, Jul 24 2009