A099672 Partial sums of repdigits of A002279.

5, 60, 615, 6170, 61725, 617280, 6172835, 61728390, 617283945, 6172839500, 61728395055, 617283950610, 6172839506165, 61728395061720, 617283950617275, 6172839506172830, 61728395061728385, 617283950617283940, 6172839506172839495, 61728395061728395050, 617283950617283950605

Offset: 1

Author

Labos Elemer, Nov 17 2004

Keywords

• base
• nonn
• easy

Examples

			5 + 55 + 555 + 5555 + 55555 = a(5) = 61725.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..999
• Index entries for linear recurrences with constant coefficients, signature (12,-21,10).

Crossrefs

Cf. A002275-A002283, A014824, A057932, A099669-A099675.

Programs

Mathematica

<Robert G. Wilson v, Nov 20 2004 *)
Accumulate[Table[FromDigits[PadRight[{},n,5]],{n,0,20}]] (* Harvey P. Dale, Oct 05 2013 *)

PARI

Vec(5*x/((1 - x)^2*(1 - 10*x)) + O(x^40)) \\ Colin Barker, Nov 30 2017

Formula

a(n) = (5/81)*(10^(n+1) - 9*n - 10). - R. Piyo (nagoya314(AT)yahoo.com), Dec 10 2004.

From Colin Barker, Nov 30 2017: (Start)

G.f.: 5*x/((1 - x)^2*(1 - 10*x)).

a(n) = 12*a(n-1) - 21*a(n-2) + 10*a(n-3) for n > 3. (End)

From Elmo R. Oliveira, Apr 03 2025: (Start)

E.g.f.: 5*exp(x)*(10*exp(9*x) - 9*x - 10)/81.

a(n) = 5*A014824(n). (End)