A168379 - OEIS

%I #25 Mar 19 2024 09:33:04

%S 7,7,15,15,23,23,31,31,39,39,47,47,55,55,63,63,71,71,79,79,87,87,95,

%T 95,103,103,111,111,119,119,127,127,135,135,143,143,151,151,159,159,

%U 167,167,175,175,183,183,191,191,199,199,207,207,215,215,223,223,231,231

%N a(n) = 4*n - 2*(-1)^n + 1.

%H Vincenzo Librandi, <a href="/A168379/b168379.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).

%F a(n) = 8*n - a(n-1) - 2, with n>1, a(1)=7.

%F G.f.: x*(7 + x^2)/((1+x)*(1-x)^2). - _Vincenzo Librandi_, Sep 18 2013

%F a(n) = a(n-1) +a(n-2) -a(n-3). - _Vincenzo Librandi_, Sep 18 2013

%F a(n) = 7 + 8*floor((n-1)/2). - _Bruno Berselli_, Sep 18 2013

%F E.g.f.: (-2 + exp(x) + (4*x + 1)*exp(2*x))*exp(-x). - _G. C. Greubel_, Jul 19 2016

%p A168379:=n->4*n - 2*(-1)^n + 1: seq(A168379(n), n=1..100); # _Wesley Ivan Hurt_, Apr 26 2017

%t Table[4 n - 2 (-1)^n + 1, {n, 60}] (* _Bruno Berselli_, Sep 18 2013 *)

%t CoefficientList[Series[(7 + x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* _Vincenzo Librandi_, Sep 18 2013 *)

%o (Magma) [4*n -2*(-1)^n + 1: n in [1..70]]; // _Vincenzo Librandi_, Sep 18 2013

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Nov 24 2009

%E Definition rewritten by _Vincenzo Librandi_, Sep 18 2013