A131738 - OEIS

%I #13 Dec 03 2022 19:24:58

%S 0,-2,3,-4,5,-6,7,-8,9,-10,11,-12,13,-14,15,-16,17,-18,19,-20,21,-22,

%T 23,-24,25,-26,27,-28,29,-30,31,-32,33,-34,35,-36,37,-38,39,-40,41,

%U -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

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

%C Also the main diagonal of A138057.

%H G. C. Greubel, <a href="/A131738/b131738.txt">Table of n, a(n) for n = 0..5000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-2,-1).

%F From _G. C. Greubel_, Nov 02 2017: (Start)

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

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

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

%t Join[{0}, Table[(-1)^n*(n + 1), {n, 1, 50}]] (* _G. C. Greubel_, Nov 02 2017 *)

%t LinearRecurrence[{-2,-1},{0,-2,3},80] (* _Harvey P. Dale_, Dec 03 2022 *)

%o (PARI) a(n)=if(n,(n+1)*(-1)^n,0) \\ _Charles R Greathouse IV_, Sep 01 2015

%o (Magma) [0] cat [(-1)^n*(n+1): n in [1..50]]; // _G. C. Greubel_, Nov 02 2017

%Y Cf. A105811.

%K sign,easy

%O 0,2

%A _Paul Curtz_, Sep 19 2007

%E Edited by _R. J. Mathar_, Jul 07 2008