A005051 a(n) = 8*3^n.

8, 24, 72, 216, 648, 1944, 5832, 17496, 52488, 157464, 472392, 1417176, 4251528, 12754584, 38263752, 114791256, 344373768, 1033121304, 3099363912, 9298091736, 27894275208, 83682825624, 251048476872, 753145430616, 2259436291848, 6778308875544, 20334926626632

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

For n>=3, a(n-3) is equal to the number of functions f:{1,2,...,n}->{1,2,3} such that for fixed, different x_1, x_2, x_3 in {1,2,...,n} and fixed y_1, y_2, y_3 in {1,2,3} we have f(x_i)<>y_i, (i=1,2,3). - Milan Janjic, May 13 2007

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
• Tanya Khovanova, Recursive Sequences
• Index entries for linear recurrences with constant coefficients, signature (3).

Crossrefs

Cf. A000244, A008776.

Programs

Magma

[8*3^n: n in [0..30]]; // Vincenzo Librandi, Jun 10 2011

Mathematica

8*3^Range[0, 60] (* Vladimir Joseph Stephan Orlovsky, Jun 09 2011 *)

PARI

a(n)=8*3^n \\ Charles R Greathouse IV, Sep 28 2015

Formula

a(n) = 3*a(n-1). G.f.: 8/(1-3*x). - Colin Barker, Jul 02 2012

From Elmo R. Oliveira, Aug 16 2024: (Start)

E.g.f.: 8*exp(3*x).

a(n) = 8*A000244(n) = 4*A008776(n). (End)