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 A156091 #9 Feb 02 2020 20:48:26
%S A156091 0,-1,15,-274,4910,-88115,1581149,-28372580,509125276,-9135882405,
%T A156091 163936757995,-2941725761526,52787126949450,-947226559328599,
%U A156091 16997290940965305,-305004010378046920,5473074895863879224,-98210344115171779145
%N A156091 One fourth of the alternating sum of the squares of the first n Fibonacci numbers with index divisible by 3.
%C A156091 Natural bilateral extension (brackets mark index 0): ..., 88115, -4910, 274, -15, 1, 0, [0], -1, 15, -274, 4910, -88115, 1581149, ... This is (-A156091)-reversed followed by A156091. That is, A156091(-n) = -A156091(n-1).
%H A156091 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-16,34,-16,-1).
%F A156091 Let F(n) be the Fibonacci number A000045(n).
%F A156091 a(n) = (1/4) sum_{k=1..n} (-1)^k F(3k)^2.
%F A156091 Closed form: a(n) = (-1)^n F(6n+3)/40 - (2 n + 1)/20.
%F A156091 Recurrence: a(n) + 17 a(n-1) - 17 a(n-2) - a(n-3) = -2.
%F A156091 Recurrence: a(n) + 16 a(n-1) - 34 a(n-2) + 16 a(n-3) + a(n-4) = 0.
%F A156091 G.f.: A(x) = -(x + x^2)/(1 + 16 x - 34 x^2 + 16 x^3 + x^4) = -x(1 + x)/((1 - x)^2 (1 + 18 x + x^2)).
%t A156091 a[n_Integer] := If[ n >= 0, Sum[ (-1)^k (1/4) Fibonacci[3k]^2, {k, 1, n} ], Sum[ -(-1)^k (1/4) Fibonacci[-3k]^2, {k, 1, -n - 1} ] ]
%Y A156091 Cf. A156084, A156085, A156090.
%K A156091 sign,easy
%O A156091 0,3
%A A156091 _Stuart Clary_, Feb 04 2009