A064756 a(n) = n*10^n - 1.

9, 199, 2999, 39999, 499999, 5999999, 69999999, 799999999, 8999999999, 99999999999, 1099999999999, 11999999999999, 129999999999999, 1399999999999999, 14999999999999999, 159999999999999999, 1699999999999999999, 17999999999999999999, 189999999999999999999, 1999999999999999999999

Offset: 1

Author

N. J. A. Sloane, Oct 19 2001

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Paul Leyland, Factors of Cullen and Woodall numbers.
• Paul Leyland, Generalized Cullen and Woodall numbers.
• Amelia Carolina Sparavigna, Some Groupoids and their Representations by Means of Integer Sequences, International Journal of Sciences (2019) Vol. 8, No. 10.
• Index entries for linear recurrences with constant coefficients, signature (21,-120,100).

Crossrefs

Cf. for a(n) = n*k^n - 1: -A000012 (k=0), A001477 (k=1), A003261 (k=2), A060352 (k=3), A060416 (k=4), A064751 (k=5), A064752 (k=6), A064753 (k=7), A064754 (k=8), A064755 (k=9), this sequence (k=10), A064757 (k=11), A064758 (k=12).

Cf. A064748, A126431.

Programs

Magma

[ n*10^n-1: n in [1..20]]; // Vincenzo Librandi, Sep 16 2011

Maple

k:= 10; f:= gfun:-rectoproc({1 + (k-1)*n + k*n*a(n-1) - (n-1)*a(n) = 0, a(1) = k-1}, a(n), remember): map(f, [$1..20]); # Georg Fischer, Feb 19 2021

Mathematica

Array[# 10^# - 1 &, 18] (* Michael De Vlieger, Jan 14 2020 *)

Formula

From Elmo R. Oliveira, Sep 07 2024: (Start)

G.f.: x*(100*x^2 - 10*x - 9)/((x - 1)*(10*x - 1)^2).

E.g.f.: 1 + exp(x)*(10*x*exp(9*x) - 1).

a(n) = 21*a(n-1) - 120*a(n-2) + 100*a(n-3) for n > 3.

a(n) = A126431(n) - 1 = A064748(n) - 2. (End)