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

0,2

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).

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A061690 A133678 A005548 * A238103 A200978 A361572

Adjacent sequences: A059407 A059408 A059409 * A059411 A059412 A059413

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 30 2001

Status

approved