A168210 a(n) = 6*n - a(n-1) + 1 with n>1, a(1)=0.

0, 13, 6, 19, 12, 25, 18, 31, 24, 37, 30, 43, 36, 49, 42, 55, 48, 61, 54, 67, 60, 73, 66, 79, 72, 85, 78, 91, 84, 97, 90, 103, 96, 109, 102, 115, 108, 121, 114, 127, 120, 133, 126, 139, 132, 145, 138, 151, 144, 157, 150, 163, 156, 169, 162, 175, 168, 181, 174, 187

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) = 3*n + 2 + 5*(-1)^n. - Jon E. Schoenfield, Jun 24 2010

G.f.: x^2*(13-7*x)/((1+x)*(1-x)^2). - Bruno Berselli, Feb 28 2012

E.g.f.: (5 - 7*exp(x) + (2 + 3*x)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 15 2016

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

Mathematica

LinearRecurrence[{1, 1, -1}, {0, 13, 6}, 30] (* Vincenzo Librandi, Feb 27 2012 *)
nxt[{n_, a_}]:={n+1, 6(n+1)-a+1}; NestList[nxt, {1, 0}, 60][[All, 2]] (* Harvey P. Dale, Aug 20 2021 *)

Prog

(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

Crossrefs

Sequence in context: A322569 A004478 A300504 * A206612 A220131 A268723

Adjacent sequences: A168207 A168208 A168209 * A168211 A168212 A168213

Keyword

nonn,easy

Author

Vincenzo Librandi, Nov 20 2009

Status

approved