A059410 J_n(9) (see A059379).

0, 6, 72, 702, 6480, 58806, 530712, 4780782, 43040160, 387400806, 3486725352, 31380882462, 282429005040, 2541864234006, 22876787671992, 205891117745742, 1853020145805120, 16677181570526406, 150094634909578632, 1350851716510730622, 12157665455570144400, 109418989121052006006

Offset: 0

Author

N. J. A. Sloane, Jan 30 2001

Keywords

• nonn
• easy

References

• L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 199, #3.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (12,-27).

Crossrefs

Cf. A000244, A016142, A024023, A059379, A059380, A059409.

Programs

Magma

[9^n-3^n: n in [0..20]]; // Vincenzo Librandi, Jun 03 2011

Maple

A059410:=n->9^n-3^n: seq(A059410(n), n=0..30); # Wesley Ivan Hurt, Aug 16 2016

Mathematica

Table[9^n - 3^n, {n, 0, 25}] (* or *) CoefficientList[Series[6 x /((1 - 3 x) (1 - 9 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 04 2014 *)

Formula

a(n) = 9^n - 3^n; a(n) = 12*a(n-1) - 27*a(n-2) for n > 1. - Vincenzo Librandi, Jun 03 2011

From Vincenzo Librandi, Oct 04 2014: (Start)

a(n) = 3^n*(3^n-1) = A000244(n)*A024023(n).

G.f.: 6*x/((1-3*x)*(1-9*x)). (End)

a(n) = 6*A016142(n). - R. J. Mathar, Nov 23 2018

E.g.f.: 2*exp(6*x)*sinh(3*x). - Elmo R. Oliveira, Mar 31 2025