A133125 a(n) = (7*3^n - (-3)^n)/6.

1, 4, 9, 36, 81, 324, 729, 2916, 6561, 26244, 59049, 236196, 531441, 2125764, 4782969, 19131876, 43046721, 172186884, 387420489, 1549681956, 3486784401, 13947137604, 31381059609, 125524238436, 282429536481, 1129718145924, 2541865828329, 10167463313316

Offset: 0

Author

Gary W. Adamson, Sep 19 2007

Keywords

• nonn
• easy

Comments

A133647 is a companion sequence.

Examples

			a(4) = 3^4 = 81.
a(5) = 324 = 4 * 3^4.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,9).

Crossrefs

Cf. A000244, A038754, A133080, A133647.

Programs

Mathematica

Table[3^(n - 2) ((-1)^n + 7)/2, {n, 1, 60}] (* Vladimir Joseph Stephan Orlovsky, Jun 10 2011 *)
LinearRecurrence[{0,9},{1,4},30] (* Harvey P. Dale, Mar 27 2017 *)

PARI

a(n) =  (7*3^n - (-3)^n)/6 \\ Andrew Howroyd, Jul 03 2024

Formula

A133080 * A000244, where A000244 = (3^0, 3^1, 3^2, ...).

For even n, a(n) = 3^n. For odd n, a(n) = 4 * 3^(n-1).

From R. J. Mathar, Oct 30 2008: (Start)

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

a(n) = 9*a(n-2). (End)

a(n) = A038754(n)^2. - T. D. Noe, Jun 10 2011

E.g.f.: (3*exp(3*x) + sinh(3*x))/3. - Andrew Howroyd, Jul 03 2024

From Amiram Eldar, Jun 02 2025: (Start)

Sum_{n>=0} 1/a(n) = 45/32.

Sum_{n>=0} (-1)^n/a(n) = 27/32. (End)

Extensions

Name changed by Andrew Howroyd, Jul 03 2024