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A162436
a(n) = 3*a(n-2) for n > 2; a(1) = 1, a(2) = 3.
13
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, 1162261467
OFFSET
1,2
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.
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
E.g.f.: cosh(sqrt(3)*x) - 1 + sinh(sqrt(3)*x)/sqrt(3). - Stefano Spezia, Dec 31 2022
MATHEMATICA
CoefficientList[Series[(-3*x - 1)/(3*x^2 - 1), {x, 0, 200}], x] (* Vladimir Joseph Stephan Orlovsky, Jun 10 2011 *)
Transpose[NestList[{Last[#], 3*First[#]}&, {1, 3}, 40]][[1]] (* or *) With[{c= 3^Range[20]}, Join[{1}, Riffle[c, c]]](* Harvey P. Dale, Feb 17 2012 *)
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
CROSSREFS
Cf. A000244 (powers of 3), A128019 (expansion of (1-3x)/(1+3x^2)), A164123, A026150, A001834, A030192, A161728, A162272.
Essentially the same as A056449 (3^floor((n+1)/2)) and A108411 (powers of 3 repeated).
Sequence in context: A128019 A056449 A108411 * A146788 A147244 A146575
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, Jul 03 2009, Jul 05 2009
EXTENSIONS
G.f. corrected, formula simplified, comments added by Klaus Brockhaus, Sep 18 2009
STATUS
approved