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

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

Offset

0,1

Comments

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

Number n such that if a=n, b=8n, c=15n, d=36n*sqrt(3n), 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).

Formula

From Philippe Deléham, Nov 23 2008: (Start)

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

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

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000244.

Sequence in context: A035088 A344724 A268094 * A102518 A361842 A168495

Adjacent sequences: A013705 A013706 A013707 * A013709 A013710 A013711

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved