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A092270
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If n mod 2 == 0 then 3^n else 2^n.
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0
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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
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OFFSET
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0,2
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COMMENTS
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The convergent series 1/2 + 1/9 + 1/8 + 1/81 + 1/32 + ... fails the ratio test.
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REFERENCES
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B. R. Gelbaum and J. M. H. Olmsted, Counterexamples in Analysis, Holden-Day, San Francisco, 1964; see p. 60.
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LINKS
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Table of n, a(n) for n=0..30.
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FORMULA
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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)
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MATHEMATICA
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Table[ If[ EvenQ[n], 3^n, 2^n], {n, 0, 30}] (* Robert G. Wilson v, Feb 18 2004 *)
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PROG
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(PARI) a(n) = if (n%2, 2^n, 3^n); \\ Michel Marcus, Jul 06 2022
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CROSSREFS
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Cf. A000079, A000244.
Sequence in context: A092397 A272348 A351166 * A249225 A191351 A324553
Adjacent sequences: A092267 A092268 A092269 * A092271 A092272 A092273
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Feb 16 2004
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STATUS
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approved
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