A168301 a(n) = (6*n + 3*(-1)^n - 1)/2.

1, 7, 7, 13, 13, 19, 19, 25, 25, 31, 31, 37, 37, 43, 43, 49, 49, 55, 55, 61, 61, 67, 67, 73, 73, 79, 79, 85, 85, 91, 91, 97, 97, 103, 103, 109, 109, 115, 115, 121, 121, 127, 127, 133, 133, 139, 139, 145, 145, 151, 151, 157, 157, 163, 163, 169, 169, 175, 175, 181, 181

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).

Crossrefs

Cf. A016921, A168328, A168286.

Programs

Magma

[n eq 1 select 1 else 6*n-Self(n-1)-4: n in [1..70]]; // Vincenzo Librandi, Sep 17 2013

Mathematica

Table[3 n + 3 (-1)^n/2 - 1/2, {n, 70}] (* Bruno Berselli, Sep 17 2013 *)
CoefficientList[Series[(1 + 6 x - x^2)/((1 + x) (1 - x)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 17 2013 *)

Formula

a(n) = 6*n - a(n-1) - 4, with n>1, a(1)=1.

From Vincenzo Librandi, Sep 17 2013: (Start)

G.f.: x*(1 + 6*x - x^2)/((1+x)*(1-x)^2).

a(n) = A168286(n) - 1 = A168328(n) + 1.

a(n) = a(n-1) +a(n-2) -a(n-3). (End)

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

Extensions

New definition by Bruno Berselli, Sep 17 2013