A162766 a(n) = 3*a(n-2) for n > 2; a(1) = 4, a(2) = 3.

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, Jul 13 2009

Keywords

• nonn

Comments

Binomial transform is A162559. Second binomial transform is A077236.

Links

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

Crossrefs

Cf. A074324, A166552, A162559, A077236, A162436.

Programs

Magma

[ n le 2 select 5-n else 3*Self(n-2): n in [1..34] ];

PARI

a(n)=3^(n\2)*4^(n%2) \\ M. F. Hasler, Dec 03 2014

Formula

a(n) = (5-3*(-1)^n)*3^(1/4*(2*n-1+(-1)^n))/2.

G.f.: x*(4+3*x)/(1-3*x^2).

a(n) = A074324(n+1) = A166552(n+1) = 3^floor(n/2)*4^(n%2), where n%2 = 0 for n even, 1 for n odd. - M. F. Hasler, Dec 03 2014

Extensions

G.f. corrected by Klaus Brockhaus, Sep 18 2009