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
Links
- G. C. Greubel, Table of n, a(n) for n = 0..5000
- Index entries for linear recurrences with constant coefficients, signature (-2,-1).
Programs
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Magma
[0] cat [(-1)^n*(n+1): n in [1..50]]; // G. C. Greubel, Nov 02 2017
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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 *) -
PARI
a(n)=if(n,(n+1)*(-1)^n,0) \\ Charles R Greathouse IV, Sep 01 2015
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)
Extensions
Edited by R. J. Mathar, Jul 07 2008
Comments