A168300 a(n) = 6*n - a(n-1) - 2 with a(1)=5.

5, 5, 11, 11, 17, 17, 23, 23, 29, 29, 35, 35, 41, 41, 47, 47, 53, 53, 59, 59, 65, 65, 71, 71, 77, 77, 83, 83, 89, 89, 95, 95, 101, 101, 107, 107, 113, 113, 119, 119, 125, 125, 131, 131, 137, 137, 143, 143, 149, 149, 155, 155, 161, 161, 167, 167, 173, 173, 179, 179

Offset: 1

Author

Vincenzo Librandi, Nov 22 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).

Programs

Magma

[n le 2 select 5 else 6*n-Self(n-1)-2: n in [1..60]];  // Bruno Berselli, Apr 14 2011

Mathematica

Table[(6*n-3*(-1)^n+1)/2,{n,1,70}] (* Vincenzo Librandi, Feb 22 2012 *)
LinearRecurrence[{1,1,-1},{5,5,11}, 50] (* G. C. Greubel, Jul 17 2016 *)

Formula

From R. J. Mathar, Jan 03 2011: (Start)

a(n+1) = A016969(floor(n/2)).

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

a(n) = (6*n - 3*(-1)^n + 1)/2. - Bruno Berselli, Apr 14 2011

E.g.f.: (1/2)*(-3 + 2*exp(x) + (1 + 6*x)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 17 2016

Extensions

G.f. corrected by Bruno Berselli, Apr 14 2011