A168210 - OEIS

%I #27 Feb 23 2023 03:45:55

%S 0,13,6,19,12,25,18,31,24,37,30,43,36,49,42,55,48,61,54,67,60,73,66,

%T 79,72,85,78,91,84,97,90,103,96,109,102,115,108,121,114,127,120,133,

%U 126,139,132,145,138,151,144,157,150,163,156,169,162,175,168,181,174,187

%N a(n) = 6*n - a(n-1) + 1 with n>1, a(1)=0.

%H Vincenzo Librandi, <a href="/A168210/b168210.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) = 3*n + 2 + 5*(-1)^n. - _Jon E. Schoenfield_, Jun 24 2010

%F G.f.: x^2*(13-7*x)/((1+x)*(1-x)^2). - _Bruno Berselli_, Feb 28 2012

%F E.g.f.: (5 - 7*exp(x) + (2 + 3*x)*exp(2*x))*exp(-x). - _G. C. Greubel_, Jul 15 2016

%F Sum_{n>=2} (-1)^(n+1)/a(n) = 8/7 - Pi/(4*sqrt(3)) - log(2)/3 - log(3)/4. - _Amiram Eldar_, Feb 23 2023

%t LinearRecurrence[{1, 1, -1}, {0, 13, 6}, 30] (* _Vincenzo Librandi_, Feb 27 2012 *)

%t nxt[{n_,a_}]:={n+1,6(n+1)-a+1}; NestList[nxt,{1,0},60][[All,2]] (* _Harvey P. Dale_, Aug 20 2021 *)

%o (Magma) I:=[0, 13, 6]; [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

%K nonn,easy

%O 1,2

%A _Vincenzo Librandi_, Nov 20 2009