A099674 Partial sums of repdigits of A002281.

0, 7, 84, 861, 8638, 86415, 864192, 8641969, 86419746, 864197523, 8641975300, 86419753077, 864197530854, 8641975308631, 86419753086408, 864197530864185, 8641975308641962, 86419753086419739, 864197530864197516, 8641975308641975293, 86419753086419753070, 864197530864197530847

Offset: 0

Author

Labos Elemer, Nov 17 2004

Keywords

• base
• nonn
• easy

Examples

			7 + 77 + 777 + 7777 + 77777 = a(5) = 86415.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• 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[LinearRecurrence[{11,-10},{0,7},25]] (* Harvey P. Dale, Jul 22 2025 *)

Formula

a(n) = (7/81)*(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.: 7*x/((1 - x)^2*(1 - 10*x)).

E.g.f.: 7*exp(x)*(10*exp(9*x) - 9*x - 10)/81.

a(n) = 7*A014824(n).

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

Extensions

More terms from Elmo R. Oliveira, Apr 02 2025

a(0)=0 prepended by Harvey P. Dale, Jul 22 2025