OFFSET
0,1
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).
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
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved