A005030 a(n) = 5*3^n.

5, 15, 45, 135, 405, 1215, 3645, 10935, 32805, 98415, 295245, 885735, 2657205, 7971615, 23914845, 71744535, 215233605, 645700815, 1937102445, 5811307335, 17433922005, 52301766015, 156905298045, 470715894135, 1412147682405, 4236443047215, 12709329141645

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
• Tanya Khovanova, Recursive Sequences
• Jeffrey Ward, Does Ten Have a Friend?, arXiv:0806.1001 [math.NT], 2008.
• Index entries for linear recurrences with constant coefficients, signature (3).

Crossrefs

Cf. A000244.

Programs

Magma

[5*3^n: n in [0..30]]; // Vincenzo Librandi, Jun 10 2011

Mathematica

5*3^Range[0, 60] (* Vladimir Joseph Stephan Orlovsky, Jun 09 2011 *)

PARI

a(n)=5*3^n \\ Charles R Greathouse IV, Oct 07 2015

Formula

O.g.f.: 5/(1-3*x). - R. J. Mathar, Jan 31 2008

Limit_{n->oo} sigma(a(n))/a(n) = 9/5 = sigma(10)/10 (see Ward link). - Michel Marcus, Apr 30 2013

G.f.: 1/x + 2 - 2/x/G(0), where G(k)= 1 + 1/(1 - x*(5*k-3)/(x*(5*k+2) - 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 04 2013

a(n) = 5*A000244(n). - Michel Marcus, Aug 25 2016

E.g.f.: 5*exp(3*x). - Stefano Spezia, Aug 28 2023