A114753 First column of A114751.

1, 3, 3, 7, 5, 11, 7, 15, 9, 19, 11, 23, 13, 27, 15, 31, 17, 35, 19, 39, 21, 43, 23, 47, 25, 51, 27, 55, 29, 59, 31, 63, 33, 67, 35, 71, 37, 75, 39, 79, 41, 83, 43, 87, 45, 91, 47, 95, 49, 99, 51, 103, 53, 107, 55, 111, 57, 115, 59, 119, 61, 123, 63, 127, 65, 131, 67, 135, 69

Offset: 1

Author

Amarnath Murthy, Nov 15 2005

Keywords

• easy
• nonn

Comments

A114752, (1, 2, 5, 4, 9, 6, ...) + A114753 - (1,1,1,...) = 3n+1: (1, 4, 7, 10, 13, ...). - Gary W. Adamson, Sep 16 2007

First column of table A210530. - Boris Putievskiy, Jan 29 2013

Links

• Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Crossrefs

Cf. A114751, A114752.

Cf. A133080, A210530.

Programs

Mathematica

Table[If[OddQ[n],n,2n-1],{n,1,120}] (* Vladimir Joseph Stephan Orlovsky, Apr 02 2011*)

Formula

a(2n+1) = 2n+1, a(2n) = 4n-1.

a(n) = 2*a(n-2) - a(n-4). - Joerg Arndt, Apr 02 2011

Equals A133080 * [1,2,3,...]. - Gary W. Adamson, Sep 08 2007

G.f. x*(1+3*x+x^2+x^3) / ( (x-1)^2*(1+x)^2 ). - R. J. Mathar, Apr 04 2012

a(n) = (3*n-1-(n-1)*(-1)^(n-1))/2. - Boris Putievskiy, Jan 29 2013

Extensions

More terms from Joshua Zucker, May 05 2006