A168280 (1 - 5*(-1)^n + 10*n)/4.

4, 4, 9, 9, 14, 14, 19, 19, 24, 24, 29, 29, 34, 34, 39, 39, 44, 44, 49, 49, 54, 54, 59, 59, 64, 64, 69, 69, 74, 74, 79, 79, 84, 84, 89, 89, 94, 94, 99, 99, 104, 104, 109, 109, 114, 114, 119, 119, 124, 124, 129, 129, 134, 134, 139, 139, 144, 144, 149, 149, 154, 154, 159

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

[(1-5*(-1)^n+10*n)/4: n in [1..70]]; // Vincenzo Librandi, Sep 16 2013

Mathematica

CoefficientList[Series[(4 + x^2) / ((1 - x)^2 (1 + x)), {x, 0, 80}], x] (* Vincenzo Librandi, Sep 16 2013 *)
LinearRecurrence[{1,1,-1},{4,4,9},80] (* Harvey P. Dale, Jul 29 2022 *)

Formula

a(n) = 5*n - a(n-1) - 2, with n>1, a(1)=4.

From Colin Barker, Jun 30 2012: (Start)

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

G.f.: x*(4 + x^2)/((1-x)^2*(1+x)). (End)

E.g.f.: (1/4)*(-5 + 4*exp(x) + (1 + 10*x)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 16 2016

Extensions

New name from Colin Barker, Jun 30 2012