A168376 a(n) = (14*n - 7*(-1)^n - 9)/4.

3, 3, 10, 10, 17, 17, 24, 24, 31, 31, 38, 38, 45, 45, 52, 52, 59, 59, 66, 66, 73, 73, 80, 80, 87, 87, 94, 94, 101, 101, 108, 108, 115, 115, 122, 122, 129, 129, 136, 136, 143, 143, 150, 150, 157, 157, 164, 164, 171, 171, 178, 178, 185, 185, 192, 192, 199, 199, 206

Offset: 1

Author

Vincenzo Librandi, Nov 24 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. A168331.

Programs

Magma

[n eq 1 select 3 else 7*n-Self(n-1)-8: n in [1..70]]; // Vincenzo Librandi, Sep 17 2013

Mathematica

Table[7 n/2 - (7 (-1)^n + 9)/4, {n, 60}] (* Bruno Berselli, Sep 17 2013 *)
CoefficientList[Series[(3 + 4 x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 17 2013 *)

PARI

a(n)=(14*n-7*(-1)^n-9)/4 \\ Charles R Greathouse IV, Jul 19 2016

Formula

a(n) = 7*n - a(n-1) - 8, with n>1, a(1)=3.

a(n) = A168331(n-1), n>1. - R. J. Mathar, Nov 25 2009

G.f.: x*(3 + 4*x^2)/((1+x) * (x-1)^2). - R. J. Mathar, Nov 25 2009

a(n) = 3 + 7*floor((n-1)/2). - Bruno Berselli, Sep 18 2013

From G. C. Greubel, Jul 19 2016: (Start)

E.g.f.: (1/4)*(-7 + 16*exp(x) + (14*x - 9)*exp(2*x))*exp(-x).

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

Extensions

Definition rewritten using Mathar's formula by Bruno Berselli, Sep 17 2013