A168416 a(n) = 1 + 9*floor(n/2).

1, 10, 10, 19, 19, 28, 28, 37, 37, 46, 46, 55, 55, 64, 64, 73, 73, 82, 82, 91, 91, 100, 100, 109, 109, 118, 118, 127, 127, 136, 136, 145, 145, 154, 154, 163, 163, 172, 172, 181, 181, 190, 190, 199, 199, 208, 208, 217, 217, 226, 226, 235, 235, 244, 244, 253, 253

Offset: 1

Author

Vincenzo Librandi, Nov 25 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. A017173.

Programs

Magma

[1+9*Floor(n/2): n in [1..70]]; // Vincenzo Librandi, Sep 19 2013

Mathematica

Table[1 + 9 Floor[n/2], {n, 70}] (* or *) CoefficientList[Series[(1 + 9 x - x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 19 2013 *)

Formula

a(n) = 9*n - a(n-1) - 7, with n>1, a(1)=1.

G.f.: x*(1 + 9*x - x^2)/((1+x)*(x-1)^2). - Vincenzo Librandi, Sep 19 2013

a(n) = a(n-1) +a(n-2) -a(n-3). - Vincenzo Librandi, Sep 19 2013

E.g.f.: (1/4)*(9 - 4*exp(x) + (18*x - 5)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 22 2016

Extensions

New definition by Vincenzo Librandi, Sep 19 2013