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 A092270 If n mod 2 == 0 then 3^n else 2^n. 0
 1, 2, 9, 8, 81, 32, 729, 128, 6561, 512, 59049, 2048, 531441, 8192, 4782969, 32768, 43046721, 131072, 387420489, 524288, 3486784401, 2097152, 31381059609, 8388608, 282429536481, 33554432, 2541865828329, 134217728, 22876792454961, 536870912, 205891132094649 (list; graph; refs; listen; history; text; internal format)
 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. LINKS 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 Cf. A000079, A000244. Sequence in context: A092397 A272348 A351166 * A249225 A191351 A324553 Adjacent sequences: A092267 A092268 A092269 * A092271 A092272 A092273 KEYWORD nonn AUTHOR N. J. A. Sloane, Feb 16 2004 STATUS approved

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Last modified March 22 22:02 EDT 2023. Contains 361434 sequences. (Running on oeis4.)