A272067 a(n) = (10^n-1)^4.

0, 6561, 96059601, 996005996001, 9996000599960001, 99996000059999600001, 999996000005999996000001, 9999996000000599999960000001, 99999996000000059999999600000001, 999999996000000005999999996000000001, 9999999996000000000599999999960000000001, 99999999996000000000059999999999600000000001

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, 9^4 = 6561 and 6 + 5 + 6 + 1 = 18 * 1.

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

Examples

			From _Seiichi Manyama_, Sep 18 2018: (Start)
n| a(n) can be divided into 4 parts for n > 1.
-+--------------------------------------------
1|        65        61
2|   9   605   9   601
3|  99  6005  99  6001
4| 999 60005 999 60001
(End)
		

Links

• Index entries for linear recurrences with constant coefficients, signature (11111,-11222110,1122211000,-11111000000,10000000000).

Crossrefs

Cf. A002283, A059988, A272066, A272068, A319358.

Programs

Magma

[(10^n-1)^4 : n in [0..10]]; // Wesley Ivan Hurt, Apr 19 2016

Maple

A272067:=n->(10^n-1)^4: seq(A272067(n), n=0..15); # Wesley Ivan Hurt, Apr 19 2016

Mathematica

(10^Range[0, 10] - 1)^4 (* Wesley Ivan Hurt, Apr 19 2016 *)

PARI

a(n) = (10^n-1)^4; \\ Michel Marcus, Apr 19 2016

Ruby

(0..n).each{|i| p ('9' * i).to_i ** 4}

Formula

a(n) = A059988(n)^2 = A002283(n)^4.

From Ilya Gutkovskiy, Apr 19 2016: (Start)

O.g.f.: 6561*x*(1 + 100*x)*(1 + 3430*x + 10000*x^2)/((1 - x)*(1 - 10*x)*(1 - 100*x)*(1 - 1000*x)*(1 - 10000*x)).

E.g.f.: (1 - 4*exp(9*x) + 6*exp(99*x) - 4*exp(999*x) + exp(9999*x))*exp(x). (End)