A099673 Partial sums of repdigits of A002280.

6, 72, 738, 7404, 74070, 740736, 7407402, 74074068, 740740734, 7407407400, 74074074066, 740740740732, 7407407407398, 74074074074064, 740740740740730, 7407407407407396, 74074074074074062, 740740740740740728, 7407407407407407394, 74074074074074074060, 740740740740740740726

Offset

1,1

Links

Table of n, a(n) for n=1..21.

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

Formula

a(n) = (2/27)*(10^(n+1) - 9*n - 10). - R. Piyo (nagoya314(AT)yahoo.com), Dec 10 2004

From Elmo R. Oliveira, Apr 02 2025: (Start)

G.f.: 6*x/((1 - x)^2*(1 - 10*x)).

a(n) = 6*A014824(n).

E.g.f.: 2*exp(x)*(10*exp(9*x) - 9*x - 10)/27.

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

Example

6 + 66 + 666 + 6666 + 66666 = a(5) = 74070.

Mathematica

<<NumberTheory`NumberTheoryFunctions` Table[{k, Table[Apply[Plus, Table[k*(10^n-1)/9, {n, 1, m}]], {m, 1, 35}]}, {k, 1, 9}]
Table[6/9*Sum[10^i - 1, {i, n}], {n, 18}] (* Robert G. Wilson v, Nov 20 2004 *)

Crossrefs

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

Sequence in context: A361572 A389847 A387951 * A105928 A186665 A007031

Adjacent sequences: A099670 A099671 A099672 * A099674 A099675 A099676

Keyword

base,nonn,easy

Author

Labos Elemer, Nov 17 2004

Extensions

More terms from Elmo R. Oliveira, Apr 02 2025

Status

approved