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A166552
a(n) = 3*a(n-2) for n > 2; a(1) = 1; a(2) = 4.
3
1, 4, 3, 12, 9, 36, 27, 108, 81, 324, 243, 972, 729, 2916, 2187, 8748, 6561, 26244, 19683, 78732, 59049, 236196, 177147, 708588, 531441, 2125764, 1594323, 6377292, 4782969, 19131876, 14348907, 57395628, 43046721, 172186884, 129140163
OFFSET
1,2
COMMENTS
Interleaving of A000244 (powers of 3) and 4*A000244.
a(n) = A074324(n); A074324 has the additional term a(0)=1.
First differences are in A162852.
Second binomial transform is A054491. Fourth binomial transform is A153594.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000[Terms 1 through 300 were computed by Vincenzo Librandi; Terms 301 through 1000 by G. C. Greubel, May 17 2016]
FORMULA
a(n) = (7+(-1)^n)*3^(1/4*(2*n-5+(-1)^n))/2.
G.f.: x*(1+4*x)/(1-3*x^2).
a(n+3) = a(n+2)*a(n+1)/a(n). - Reinhard Zumkeller, Mar 04 2011
a(n) = 3^floor((n-1)/2)*4^(1-n%2). - M. F. Hasler, Dec 03 2014
E.g.f.: (sqrt(3)*sinh(sqrt(3)*x) + 4*cosh(sqrt(3)*x) - 4)/3. - Ilya Gutkovskiy, May 17 2016
MATHEMATICA
LinearRecurrence[{0, 3}, {1, 4}, 50] (* G. C. Greubel, May 17 2016 *)
PROG
(Magma) [ n le 2 select 3*n-2 else 3*Self(n-2): n in [1..35] ];
(PARI) a(n)=3^(n\2)*(4/3)^!bittest(n, 0) \\ M. F. Hasler, Dec 03 2014
CROSSREFS
Equals A162766 preceded by 1.
Cf. A000244 (powers of 3), A074324, A162852, A054491, A153594.
Sequence in context: A168430 A074324 A162766 * A122804 A122544 A323931
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Oct 16 2009
STATUS
approved