A166552 a(n) = 3*a(n-2) for n > 2; a(1) = 1; a(2) = 4.

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

Author

Klaus Brockhaus, Oct 16 2009

Keywords

• nonn

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]
• Index entries for linear recurrences with constant coefficients, signature (0,3)

Crossrefs

Equals A162766 preceded by 1.

Cf. A000244 (powers of 3), A074324, A162852, A054491, A153594.

Programs

Magma

[ n le 2 select 3*n-2 else 3*Self(n-2): n in [1..35] ];

Mathematica

LinearRecurrence[{0, 3}, {1, 4}, 50] (* G. C. Greubel, May 17 2016 *)

PARI

a(n)=3^(n\2)*(4/3)^!bittest(n,0) \\ M. F. Hasler, Dec 03 2014

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