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

1, 1, 2, 1, 3, 0, 5, -3, 10, -11, 23, -32, 57, -87, 146, -231, 379, -608, 989, -1595, 2586, -4179, 6767, -10944, 17713, -28655, 46370, -75023, 121395, -196416, 317813, -514227, 832042, -1346267, 2178311, -3524576, 5702889, -9227463, 14930354, -24157815, 39088171, -63245984, 102334157

Offset

0,3

Comments

Diagonal sums of Riordan array (1/(1-x), x/(1+x)), A112468.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Index entries for linear recurrences with constant coefficients, signature (0,2,-1).

Formula

G.f.: (1+x)/((1-x)(1+x-x^2));

a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..n-2k} C(n-k-j-1, n-2k-j)*(-1)^(n-j).

Maple

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

Mathematica

Accumulate[Table[(-1)^n Fibonacci[n-1], {n, 0, 50}]] (* Harvey P. Dale, Nov 05 2011 *)

Crossrefs

Cf. A078024.

Sequence in context: A281617 A280544 A078024 * A330502 A368213 A249455

Adjacent sequences: A112466 A112467 A112468 * A112470 A112471 A112472

Keyword

easy,sign

Author

Paul Barry, Sep 06 2005

Status

approved