%I A119283
%S A119283 0,1,0,4,5,20,44,125,316,840,2185,5736,15000,39289,102840,269260,704909,
               1845500,4831556,
%T A119283 12649205,33116020,86698896,226980625,594243024,1555748400,4073002225,
               10663258224,27916772500,73087059221,
%U A119283 191344405220,500946156380,1311494063981,3433536035500,8989114042584,23533806092185,
               61612304234040
%V A119283 0,-1,0,-4,5,-20,44,-125,316,-840,2185,-5736,15000,-39289,102840,-269260,
               704909,-1845500,4831556,
%W A119283 -12649205,33116020,-86698896,226980625,-594243024,1555748400,-4073002225,
               10663258224,-27916772500,73087059221,
%X A119283 -191344405220,500946156380,-1311494063981,3433536035500,-8989114042584,
               23533806092185,-61612304234040
%N A119283 Alternating sum of the squares of the first n Fibonacci numbers.
%C A119283 Natural bilateral extension (brackets mark index 0): ..., 840, -316, 
               125, -44, 20, -5, 4, 0, 1, 0, [0], -1, 0, -4, 5, -20, 44, -125, 316, 
               -840, 2185, ... This is (-A119283)-reversed followed by A119283.
%F A119283 Let F(n) be the Fibonacci number A000045(n).
%F A119283 a(n) = sum_{k=1..n} (-1)^k F(k)^2
%F A119283 Closed form: a(n) = (-1)^n F(2n+1)/5 - (2 n + 1)/5
%F A119283 Recurrence: a(n) + a(n-1) - 4 a(n-2) + a(n-3) + a(n-4) = 0
%F A119283 G.f.: A(x) = (-x - x^2)/(1 + x - 4 x^2 + x^3 + x^4) = -x(1 + x)/((1 - 
               x)^2 (1 + 3 x + x^2))
%F A119283 a(n)= [ -1-2*n+(-1)^n*( A001906(n+1)-A001906(n) )]/5. - R. J. Mathar 
               (mathar(AT)strw.leidenuniv.nl), Nov 16 2007
%t A119283 a[n_Integer] := If[ n >= 0, Sum[ (-1)^k Fibonacci[k]^2, {k, 1, n} ], 
               Sum[ -(-1)^k Fibonacci[ -k]^2, {k, 1, -n - 1} ] ]
%Y A119283 Cf. A001654, A119282, A119284, A119285, A119286, A119287
%Y A119283 Cf. A001654, A119282, A119284, A119285, A119286, A119287, A128696, A128698.
%Y A119283 Sequence in context: A059182 A027958 A064670 this_sequence A151499 A057781 
               A081713
%Y A119283 Adjacent sequences: A119280 A119281 A119282 this_sequence A119284 A119285 
               A119286
%K A119283 sign,easy
%O A119283 0,4
%A A119283 Stuart Clary (clary(AT)uakron.edu), May 13, 2006