A131738 a(0) = 0. a(n) = (n+1)*(-1)^n, n>0 .

0, -2, 3, -4, 5, -6, 7, -8, 9, -10, 11, -12, 13, -14, 15, -16, 17, -18, 19, -20, 21, -22, 23, -24, 25, -26, 27, -28, 29, -30, 31, -32, 33, -34, 35, -36, 37, -38, 39, -40, 41, -42, 43, -44, 45, -46, 47, -48, 49, -50, 51, -52, 53, -54, 55, -56, 57, -58, 59, -60, 61, -62, 63, -64, 65, -66, 67, -68, 69, -70, 71, -72, 73, -74, 75

Offset

0,2

Comments

Also the main diagonal of A138057.

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

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

Formula

From G. C. Greubel, Nov 02 2017: (Start)

a(n) = -2*a(n-1) - a(n-2).

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

E.g.f.: (1 - x - exp(x))*exp(-x). (End)

Mathematica

Join[{0}, Table[(-1)^n*(n + 1), {n, 1, 50}]] (* G. C. Greubel, Nov 02 2017 *)
LinearRecurrence[{-2, -1}, {0, -2, 3}, 80] (* Harvey P. Dale, Dec 03 2022 *)

Prog

(PARI) a(n)=if(n, (n+1)*(-1)^n, 0) \\ Charles R Greathouse IV, Sep 01 2015
(Magma) [0] cat [(-1)^n*(n+1): n in [1..50]]; // G. C. Greubel, Nov 02 2017

Crossrefs

Cf. A105811.

Sequence in context: A114142 A020725 A119972 * A199969 A303502 A000027

Adjacent sequences: A131735 A131736 A131737 * A131739 A131740 A131741

Keyword

sign,easy

Author

Paul Curtz, Sep 19 2007

Extensions

Edited by R. J. Mathar, Jul 07 2008

Status

approved