OFFSET
0,2
COMMENTS
The convergent series 1/2 + 1/9 + 1/8 + 1/81 + 1/32 + ... fails the ratio test.
REFERENCES
B. R. Gelbaum and J. M. H. Olmsted, Counterexamples in Analysis, Holden-Day, San Francisco, 1964; see p. 60.
FORMULA
From R. J. Mathar, Apr 28 2008: (Start)
O.g.f.: -(-1+4x^2-2x+18x^3)/((3x-1)(3x+1)(2x-1)(2x+1)).
a(n) = 13a(n-2) - 36a(n-4). (End)
From Amiram Eldar, Jul 06 2022: (Start)
Sum_{n>=0} 1/a(n) = 43/24.
Sum_{n>=0} (-1)^n/a(n) = 11/24. (End)
MATHEMATICA
Table[ If[ EvenQ[n], 3^n, 2^n], {n, 0, 30}] (* Robert G. Wilson v, Feb 18 2004 *)
PROG
(PARI) a(n) = if (n%2, 2^n, 3^n); \\ Michel Marcus, Jul 06 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 16 2004
STATUS
approved