A168373 - OEIS

%I #19 Sep 08 2022 08:45:49

%S 4,4,11,11,18,18,25,25,32,32,39,39,46,46,53,53,60,60,67,67,74,74,81,

%T 81,88,88,95,95,102,102,109,109,116,116,123,123,130,130,137,137,144,

%U 144,151,151,158,158,165,165,172,172,179,179,186,186,193,193,200,200,207

%N a(n) = 7*n - a(n-1) - 6 with n>1, a(1)=4.

%H Vincenzo Librandi, <a href="/A168373/b168373.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) = A168212(n-1), n>1. - _R. J. Mathar_, Nov 25 2009

%F From _G. C. Greubel_, Jul 19 2016: (Start)

%F a(n) = (14*n - 7 (-1)^n - 5)/4.

%F a(n) = a(n-1) + a(n-2) - a(n-3).

%F G.f.: x*(4 + 3*x^2)/((1+x)*(1 - x)^2).

%F E.g.f.: (1/4)*(-7 + 12*exp(x) + (14*x - 5)*exp(2*x))*exp(-x). (End)

%t LinearRecurrence[{1, 1, -1}, {4, 4, 11}, 60] (* _Vincenzo Librandi_, Feb 28 2012 *)

%o (Magma) I:=[4, 4, 11]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..60]]; // _Vincenzo Librandi_, Feb 28 2012

%o (PARI) a(n)=([0,1,0; 0,0,1; -1,1,1]^(n-1)*[4;4;11])[1,1] \\ _Charles R Greathouse IV_, Jul 19 2016

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Nov 24 2009