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A112469 Partial sums of (-1)^n*Fibonacci(n-1).

%I A112469 #20 Apr 17 2025 09:49:49
%S A112469 1,1,2,1,3,0,5,-3,10,-11,23,-32,57,-87,146,-231,379,-608,989,-1595,
%T A112469 2586,-4179,6767,-10944,17713,-28655,46370,-75023,121395,-196416,
%U A112469 317813,-514227,832042,-1346267,2178311,-3524576,5702889,-9227463,14930354,-24157815,39088171,-63245984,102334157
%N A112469 Partial sums of (-1)^n*Fibonacci(n-1).
%C A112469 Diagonal sums of Riordan array (1/(1-x), x/(1+x)), A112468.
%H A112469 Vincenzo Librandi, <a href="/A112469/b112469.txt">Table of n, a(n) for n = 0..300</a>
%H A112469 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,-1).
%F A112469 G.f.: (1+x)/((1-x)*(1+x-x^2)).
%F A112469 a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..n-2k} C(n-k-j-1, n-2k-j)*(-1)^(n-j).
%F A112469 From _G. C. Greubel_, Apr 17 2025: (Start)
%F A112469 a(n) = 2 + (-1)^n*Fibonacci(n-2).
%F A112469 E.g.f.: 2*exp(x) - exp(-x/2)*( cosh(sqrt(5)*x/2) + (3/sqrt(5))*sinh(sqrt(5)*x/2) ). (End)
%p A112469 a[0]:=1:a[1]:=1:a[2]:=2:a[3]:=1:for n from 4 to 50 do a[n]:=2*a[n-2]-a[n-3] od: seq(a[n], n=0..42); # _Zerinvary Lajos_, Apr 04 2008
%t A112469 Accumulate[Table[(-1)^n Fibonacci[n-1],{n,0,50}]] (* _Harvey P. Dale_, Nov 05 2011 *)
%t A112469 Table[2 +(-1)^n*Fibonacci[n-2], {n,0,50}] (* _G. C. Greubel_, Apr 17 2025 *)
%o A112469 (Magma)
%o A112469 A112469:= func< n | 2 + (-1)^n*Fibonacci(n-2) >;
%o A112469 [A112469(n): n in [0..40]]; // _G. C. Greubel_, Apr 17 2025
%o A112469 (SageMath)
%o A112469 def A112469(n): return 2+(-1)^n*fibonacci(n-2)
%o A112469 print([A112469(n) for n in range(41)]) # _G. C. Greubel_, Apr 17 2025
%Y A112469 Cf. A000045, A078024, A112468.
%K A112469 easy,sign
%O A112469 0,3
%A A112469 _Paul Barry_, Sep 06 2005