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 A119282 #50 Sep 08 2022 08:45:25
%S A119282 0,-1,0,-2,1,-4,4,-9,12,-22,33,-56,88,-145,232,-378,609,-988,1596,
%T A119282 -2585,4180,-6766,10945,-17712,28656,-46369,75024,-121394,196417,
%U A119282 -317812,514228,-832041,1346268,-2178310,3524577,-5702888,9227464,-14930353,24157816,-39088170,63245985,-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.
%C A119282 Alternating sums of rows of the triangle in A141169. - _Reinhard Zumkeller_, Mar 22 2011
%H A119282 Reinhard Zumkeller, <a href="/A119282/b119282.txt">Table of n, a(n) for n = 0..1000</a>
%H A119282 Kyu-Hwan Lee, Se-jin Oh, <a href="http://arxiv.org/abs/1601.06685">Catalan triangle numbers and binomial coefficients</a>, arXiv:1601.06685 [math.CO], 2016.
%H A119282 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,-1)
%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. - _Rick L. Shepherd_, Aug 12 2009
%t A119282 FoldList[#1 - Fibonacci@ #2 &, -Range@ 50] (* _Michael De Vlieger_, Jan 27 2016 *)
%t A119282 Accumulate[Table[(-1)^n Fibonacci[n], {n, 0, 49}]] (* _Alonso del Arte_, Apr 25 2017 *)
%o A119282 (PARI) a(n) = sum(k=1, n, (-1)^k*fibonacci(k)); \\ _Michel Marcus_, Jan 27 2016
%o A119282 (Magma) [0] cat [(&+[(-1)^k*Fibonacci(k):k in [1..n]]): n in [1..30]]; // _G. C. Greubel_, Jan 17 2018
%Y A119282 Cf. A000071, A008346, A119283, A119284, A119285, A119286, A119287.
%Y A119282 Cf. A128696, A128698.
%K A119282 sign,easy
%O A119282 0,4
%A A119282 _Stuart Clary_, May 13 2006