A168195 a(n) = 2*n - a(n-1) + 1 with n>1, a(1)=5.

5, 0, 7, 2, 9, 4, 11, 6, 13, 8, 15, 10, 17, 12, 19, 14, 21, 16, 23, 18, 25, 20, 27, 22, 29, 24, 31, 26, 33, 28, 35, 30, 37, 32, 39, 34, 41, 36, 43, 38, 45, 40, 47, 42, 49, 44, 51, 46, 53, 48, 55, 50, 57, 52, 59, 54, 61, 56, 63, 58, 65, 60, 67, 62, 69, 64, 71, 66, 73

Offset: 1

Author

Vincenzo Librandi, Nov 20 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Cf. A004442, A147677.

Programs

Magma

I:=[5,0,7]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 27 2012

Maple

A168195:=n->n+1-3*(-1)^n; seq(A168195(n), n=1..100); # Wesley Ivan Hurt, Dec 13 2013

Mathematica

LinearRecurrence[{1,1,-1},{5,0,7},30] (* Vincenzo Librandi, Feb 27 2012 *)

Formula

From R. J. Mathar, Nov 22 2009: (Start)

a(n) = a(n-1) + a(n-2) - a(n-3) = n + 1 - 3*(-1)^n.

G.f.: x*(5+2*x^2-5*x)/((1+x)*(x-1)^2). (End)

a(n) = n - 4 + 2^(2-(-1)^n). - Wesley Ivan Hurt, Dec 13 2013

a(n) = A004442(n-1) + 2*(1-(-1)^n) = A147677(n) - floor((n+3)/2). - Filip Zaludek, Oct 31 2016

Sum_{n>=3} (-1)^n/a(n) = 23/15 - log(2). - Amiram Eldar, Feb 23 2023