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

Offset

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..999

Index entries for linear recurrences with constant coefficients, signature (12,-21,10).

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>2.

(End)

Example

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

Mathematica

<<NumberTheory`NumberTheoryFunctions` Table[{k, Table[Apply[Plus, Table[k*(10^n-1)/9, {n, 1, m}]], {m, 1, 35}]}, {k, 1, 9}]
Table[5/9*Sum[10^i - 1, {i, n}], {n, 18}] (* Robert G. Wilson v, Nov 20 2004 *)
Accumulate[Table[FromDigits[PadRight[{}, n, 5]], {n, 0, 20}]] (* Harvey P. Dale, Oct 05 2013 *)

Prog

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

Crossrefs

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

Sequence in context: A059602 A290747 A212700 * A320361 A138134 A283779

Adjacent sequences: A099669 A099670 A099671 * A099673 A099674 A099675

Keyword

base,nonn,easy

Author

Labos Elemer, Nov 17 2004

Status

approved