A168197 - OEIS

%I #27 Feb 23 2023 03:46:28

%S 0,7,3,10,6,13,9,16,12,19,15,22,18,25,21,28,24,31,27,34,30,37,33,40,

%T 36,43,39,46,42,49,45,52,48,55,51,58,54,61,57,64,60,67,63,70,66,73,69,

%U 76,72,79,75,82,78,85,81,88,84,91,87,94,90,97,93,100,96,103,99,106,102

%N a(n) = 3*n - a(n-1) + 1 with n > 1, a(1)=0.

%H Vincenzo Librandi, <a href="/A168197/b168197.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) = (6*n + 5 + 11*(-1)^n)/4. - _Jon E. Schoenfield_, Jun 24 2010

%F a(n) = a(n-1) + a(n-2) - a(n-3). - _Vincenzo Librandi_, Feb 28 2012

%F G.f.: x^2*(7-4*x)/((1+x)*(1-x)^2). - _Bruno Berselli_, Feb 28 2012

%F Sum_{n>=2} (-1)^(n+1)/a(n) = 5/4 - Pi/(6*sqrt(3)) - log(3)/2. - _Amiram Eldar_, Feb 23 2023

%t LinearRecurrence[{1, 1, -1}, {0, 7, 3}, 100] (* _Vincenzo Librandi_, Feb 28 2012 *)

%o (Magma) I:=[0, 7, 3]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..70]]; // _Vincenzo Librandi_, Feb 28 2012

%K nonn,easy

%O 1,2

%A _Vincenzo Librandi_, Nov 20 2009

%E Partially edited by _N. J. A. Sloane_, Jun 25 2010