A013708 a(n) = 3^(2*n+1).

3, 27, 243, 2187, 19683, 177147, 1594323, 14348907, 129140163, 1162261467, 10460353203, 94143178827, 847288609443, 7625597484987, 68630377364883, 617673396283947, 5559060566555523, 50031545098999707, 450283905890997363, 4052555153018976267, 36472996377170786403

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

1/3 + 1/27 + 1/243 + ... = 3/8. - Gary W. Adamson, Aug 29 2008

Number k such that if a=k, b=8*k, c=15*k, d=36*k*sqrt(3*k), then a^3 + b^3 + c^3 = d^2; e.g.: a=3, b=24, c=45, d=324, 3^3 + 24^3 + 45^3 = 324^2. - Vincenzo Librandi, Nov 20 2010

Links

• Delbert L. Johnson, Table of n, a(n) for n = 0..1047
• Tanya Khovanova, Recursive Sequences.
• R. J. Mathar, Counting Walks on Finite Graphs, Nov 2020, Section 4.
• Index entries for linear recurrences with constant coefficients, signature (9).

Crossrefs

Cf. A000244.

Programs

Mathematica

NestList[9#&,3,20] (* Harvey P. Dale, Apr 21 2014 *)

PARI

a(n)=3^(2*n+1) \\ Charles R Greathouse IV, Aug 05 2015

Python

print([3**(2*n+1) for n in range(18)]) # Michael S. Branicky, Mar 27 2021

Formula

From Philippe Deléham, Nov 23 2008: (Start)

a(n) = 9*a(n-1), n > 0; a(0)=3.

G.f.: 3/(1-9*x). (End)

a(n) = A000244(2*n+1). - R. J. Mathar, Jul 10 2015

E.g.f.: 3*exp(9*x). - Stefano Spezia, Jul 09 2024