A272066 a(n) = (10^n-1)^3.

0, 729, 970299, 997002999, 999700029999, 999970000299999, 999997000002999999, 999999700000029999999, 999999970000000299999999, 999999997000000002999999999, 999999999700000000029999999999, 999999999970000000000299999999999, 999999999997000000000002999999999999

Offset: 0

Author

Seiichi Manyama, Apr 19 2016

Keywords

• nonn
• easy

Comments

The sum of the digits of a(n) is divisible by 18. For example, 9^3 = 729 and 7 + 2 + 9 = 18 * 1.

Number of 9 in a(n) is 2*n-1 for n > 0. - Seiichi Manyama, Sep 18 2018

Examples

			From _Seiichi Manyama_, Sep 18 2018: (Start)
n| a(n) can be divided into 3 parts for n > 1.
-+--------------------------------------------
1|        72    9
2|   9   702   99
3|  99  7002  999
4| 999 70002 9999
(End)
		

Links

• Index entries for linear recurrences with constant coefficients, signature (1111,-112110,1111000,-1000000).

Crossrefs

Cf. A002283, A059988, A272067, A272068, A319358.

Programs

Magma

[(10^n-1)^3 : n in [0..10]]; // Wesley Ivan Hurt, Apr 19 2016

Maple

A272066:=n->(10^n-1)^3: seq(A272066(n), n=0..15); # Wesley Ivan Hurt, Apr 19 2016

Mathematica

(10^Range[0, 10] - 1)^3 (* Wesley Ivan Hurt, Apr 19 2016 *)

PARI

a(n) = (10^n-1)^3; \\ Michel Marcus, Apr 19 2016

Ruby

(0..n).each{|i| p ('9' * i).to_i ** 3}

Formula

a(n) = A002283(n)^3.

From Ilya Gutkovskiy, Apr 19 2016: (Start)

O.g.f.: 729*x*(1 + 220*x + 1000*x^2)/((1 - x)*(1 - 10*x)*(1 - 100*x)*(1 - 1000*x)).

E.g.f.: (-1 + 3*exp(9*x) - 3*exp(99*x) + exp(999*x))*exp(x). (End)