A168209 - OEIS

%I #25 Sep 08 2022 08:45:48

%S 3,8,8,13,13,18,18,23,23,28,28,33,33,38,38,43,43,48,48,53,53,58,58,63,

%T 63,68,68,73,73,78,78,83,83,88,88,93,93,98,98,103,103,108,108,113,113,

%U 118,118,123,123,128,128,133,133,138,138,143,143,148,148,153,153,158

%N a(n) = 5*n - a(n-1) + 1 with n>1, a(1)=3.

%H Vincenzo Librandi, <a href="/A168209/b168209.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) = (10*n + 7 + 5*(-1)^n)/4. - _Jon E. Schoenfield_, Jun 24 2010

%F G.f.: x*(3+5*x-3*x^2)/((1+x)*(1-x)^2). - _Bruno Berselli_, Feb 28 2012

%F E.g.f.: (1/4)*(5 - 12*exp(x) + (7 + 10*x)*exp(2*x))*exp(-x). - _G. C. Greubel_, Jul 15 2016

%t LinearRecurrence[{1, 1, -1}, {3, 8, 8}, 30] (* _Vincenzo Librandi_, Feb 28 2012 *)

%t nxt[{n_,a_}]:={n+1,5(n+1)-a+1}; Transpose[NestList[nxt,{1,3},70]][[2]] (* _Harvey P. Dale_, Jan 23 2013 *)

%o (Magma) I:=[3, 8, 8]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..40]]; // _Vincenzo Librandi_, Feb 28 2012

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Nov 20 2009