A168197 a(n) = 3*n - a(n-1) + 1 with n > 1, a(1)=0.

0, 7, 3, 10, 6, 13, 9, 16, 12, 19, 15, 22, 18, 25, 21, 28, 24, 31, 27, 34, 30, 37, 33, 40, 36, 43, 39, 46, 42, 49, 45, 52, 48, 55, 51, 58, 54, 61, 57, 64, 60, 67, 63, 70, 66, 73, 69, 76, 72, 79, 75, 82, 78, 85, 81, 88, 84, 91, 87, 94, 90, 97, 93, 100, 96, 103, 99, 106, 102

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Formula

a(n) = (6*n + 5 + 11*(-1)^n)/4. - Jon E. Schoenfield, Jun 24 2010

a(n) = a(n-1) + a(n-2) - a(n-3). - Vincenzo Librandi, Feb 28 2012

G.f.: x^2*(7-4*x)/((1+x)*(1-x)^2). - Bruno Berselli, Feb 28 2012

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

Mathematica

LinearRecurrence[{1, 1, -1}, {0, 7, 3}, 100] (* Vincenzo Librandi, Feb 28 2012 *)

Prog

(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

Crossrefs

Sequence in context: A134883 A201329 A084000 * A257324 A138859 A257328

Adjacent sequences: A168194 A168195 A168196 * A168198 A168199 A168200

Keyword

nonn,easy

Author

Vincenzo Librandi, Nov 20 2009

Extensions

Partially edited by N. J. A. Sloane, Jun 25 2010

Status

approved