A168437 a(n) = 3 + 10*floor(n/2).

3, 13, 13, 23, 23, 33, 33, 43, 43, 53, 53, 63, 63, 73, 73, 83, 83, 93, 93, 103, 103, 113, 113, 123, 123, 133, 133, 143, 143, 153, 153, 163, 163, 173, 173, 183, 183, 193, 193, 203, 203, 213, 213, 223, 223, 233, 233, 243, 243, 253, 253, 263, 263, 273, 273, 283

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

Bisections of A168437 are A017305 and (A017305 MINUS {3}). - Rick L. Shepherd, Jun 17 2010

Programs

Magma

[3+10*Floor(n/2): n in [1..70]]; // Vincenzo Librandi, Sep 19 2013

Mathematica

Table[3 + 10 Floor[n/2], {n, 70}] (* or *) CoefficientList[Series[(3 + 10 x - 3 x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 19 2013 *)
LinearRecurrence[{1,1,-1},{3,13,13},70] (* Harvey P. Dale, May 26 2021 *)

PARI

a(n)=n\2*10+3 \\ Charles R Greathouse IV, Jan 11 2012

Formula

a(n) = 10*n - a(n-1) - 4, with n>1, a(1) = 3.

a(n) = 10*floor(n/2) + 3 = A168641(n) + 3. - Rick L. Shepherd, Jun 17 2010

G.f.: x*(3 + 10*x - 3*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

a(n) = (1 + 5*(-1)^n + 10*n)/2. - Bruno Berselli, Sep 19 2013

E.g.f.: (1/2)*(5 - 6*exp(x) + (10*x + 1)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 22 2016

Extensions

Edited by Rick L. Shepherd, Jun 17 2010

Definition rewritten, using Shepherd's formula, by Vincenzo Librandi, Sep 19 2013