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A162436
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a(n) = 3*a(n-2) for n > 2; a(1) = 1, a(2) = 3.
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10
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1, 3, 3, 9, 9, 27, 27, 81, 81, 243, 243, 729, 729, 2187, 2187, 6561, 6561, 19683, 19683, 59049, 59049, 177147, 177147, 531441, 531441, 1594323, 1594323, 4782969, 4782969, 14348907, 14348907, 43046721, 43046721, 129140163, 129140163, 387420489, 387420489
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Interleaving of A000244 and 3*A000244.
Unsigned version of A128019.
Partial sums are in A164123.
Apparently a(n) = A056449(n-1) for n > 1. a(n) = A108411(n) for n >= 1.
Binomial transform is A026150 without initial 1, second binomial transform is A001834, third binomial transform is A030192, fourth binomial transform is A161728, fifth binomial transform is A162272.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index to sequences with linear recurrences with constant coefficients, signature (0,3).
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FORMULA
| a(n) = 3^(1/4*(2*n-1+(-1)^n)).
G.f.: x*(1+3*x)/(1-3*x^2).
a(n+3) = a(n+2)*a(n+1)/a(n). [Reinhard Zumkeller, Mar 04 2011]
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MATHEMATICA
| CoefficientList[Series[(-3*x - 1)/(3*x^2 - 1), {x, 0, 200}], x] (* From Vladimir Joseph Stephan Orlovsky, Jun 10 2011 *)
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PROG
| (MAGMA) [ n le 2 select 2*n-1 else 3*Self(n-2): n in [1..35] ];
(PARI) a(n)=3^(n>>1) \\ Charles R Greathouse IV, Jul 15 2011
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CROSSREFS
| Cf. A000244 (powers of 3), A128019 (expansion of (1-3x)/(1+3x^2), A164123, A056449 (3^floor((n+1)/2)), A108411 (powers of 3 repeated), A026150, A001834, A030192, A161728, A162272.
Sequence in context: A128019 A108411 A056449 * A146788 A147244 A146575
Adjacent sequences: A162433 A162434 A162435 * A162437 A162438 A162439
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KEYWORD
| nonn,easy
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AUTHOR
| Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 03 2009, Jul 05 2009
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EXTENSIONS
| G.f. corrected, formula simplified, comments added by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Sep 18 2009
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