A168459 a(n) = (10*n + 5*(-1)^n - 3)/2.

1, 11, 11, 21, 21, 31, 31, 41, 41, 51, 51, 61, 61, 71, 71, 81, 81, 91, 91, 101, 101, 111, 111, 121, 121, 131, 131, 141, 141, 151, 151, 161, 161, 171, 171, 181, 181, 191, 191, 201, 201, 211, 211, 221, 221, 231, 231, 241, 241, 251, 251, 261, 261, 271, 271, 281

Offset: 1

Author

Vincenzo Librandi, Nov 26 2009

Keywords

• nonn
• easy
• less

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. A017281, A168457, A168282.

Programs

Magma

[1+10*Floor(n/2): n in [1..70]]; // Vincenzo Librandi, Sep 19 2013

Mathematica

Table[5 n + 5 (-1)^n/2 - 3/2, {n, 60}] (* Bruno Berselli, Sep 16 2013 *)
Table[1 + 10 Floor[n/2], {n, 70}] (* or *) CoefficientList[Series[(1 + 10 x - x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 19 2013 *)

Formula

a(n) = 10*n - a(n-1) - 8 with n>1, a(1)=1.

From Bruno Berselli, Sep 16 2013: (Start)

G.f.: x*(1 + 10*x - x^2)/((1+x)*(1-x)^2).

a(n) = A168457(n) - 1 = 2*A168282(n) - 1.

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

a(n) = 1 + 10*floor(n/2). - Vincenzo Librandi, Sep 19 2013

E.g.f.: (1/2)*(5 - 2*exp(x) + (10*x - 3)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 23 2016

Extensions

New definition by Bruno Berselli, Sep 16 2013