%I A119282
%S A119282 0,1,0,2,1,4,4,9,12,22,33,56,88,145,232,378,609,988,1596,2585,4180,6766,
               10945,17712,28656,46369,
%T A119282 75024,121394,196417,317812,514228,832041,1346268,2178310,3524577,5702888,
               9227464,14930353,24157816,39088170,
%U A119282 63245985,102334156,165580140,267914297,433494436,701408734,1134903169,
               1836311904,2971215072,4807526977,7778742048
%V A119282 0,-1,0,-2,1,-4,4,-9,12,-22,33,-56,88,-145,232,-378,609,-988,1596,-2585,
               4180,-6766,10945,-17712,28656,-46369,
%W A119282 75024,-121394,196417,-317812,514228,-832041,1346268,-2178310,3524577,
               -5702888,9227464,-14930353,24157816,-39088170,
%X A119282 63245985,-102334156,165580140,-267914297,433494436,-701408734,1134903169,
               -1836311904,2971215072,-4807526977,7778742048
%N A119282 Alternating sum of the first n Fibonacci numbers.
%C A119282 Apart from signs, same as A008346.
%C A119282 Natural bilateral extension (brackets mark index 0): ..., 88, 54, 33, 
               20, 12, 7, 4, 2, 1, 0, [0], -1, 0, -2, 1, -4, 4, -9, 12, -22, 3, 
               ... This is A000071-reversed followed by A119282.
%F A119282 Let F(n) be the Fibonacci number A000045(n).
%F A119282 a(n) = sum_{k=1..n} (-1)^k F(k)
%F A119282 Closed form: a(n) = (-1)^n F(n-1) - 1 = (-1)^n A008346(n-1)
%F A119282 Recurrence: a(n) - 2 a(n-2) + a(n-3)= 0
%F A119282 G.f.: A(x) = -x/(1 - 2 x^2 + x^3) = -x/((1 - x)(1 + x - x^2))
%F A119282 Another recurrence: a(n) = a(n-2) - a(n-1) - 1. [From Rick L. Shepherd 
               (rshepherd2(AT)hotmail.com), Aug 12 2009]
%t A119282 a[n_Integer] := If[ n >= 0, Sum[ (-1)^k Fibonacci[k], {k, 1, n} ], Sum[ 
               -(-1)^k Fibonacci[ -k], {k, 1, -n - 1} ] ]
%Y A119282 Cf. A000071, A008346, A119283, A119284, A119285, A119286, A119287
%Y A119282 Cf. A000071, A119283, A119284, A119285, A119286, A119287, A128696, A128698.
%Y A119282 Sequence in context: A074763 A099932 A008346 this_sequence A095293 A034409 
               A048049
%Y A119282 Adjacent sequences: A119279 A119280 A119281 this_sequence A119283 A119284 
               A119285
%K A119282 sign,easy
%O A119282 0,4
%A A119282 Stuart Clary (clary(AT)uakron.edu), May 13, 2006