A099671 Partial sums of repdigits of A002278.

4, 48, 492, 4936, 49380, 493824, 4938268, 49382712, 493827156, 4938271600, 49382716044, 493827160488, 4938271604932, 49382716049376, 493827160493820, 4938271604938264, 49382716049382708, 493827160493827152

Offset

1,1

Links

Table of n, a(n) for n=1..18.

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

Formula

a(n) = (4/81)*(10^(n+1) - 9*n - 10). - R. Piyo (nagoya314(AT)yahoo.com), Dec 10 2004

From Chai Wah Wu, Feb 28 2018: (Start)

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

G.f.: 4*x/((1 - x)^2*(1 - 10*x)). (End)

Example

4 + 44 + 444 + 4444 + 44444 = a(5) = 49380.

Mathematica

<<NumberTheory`NumberTheoryFunctions` Table[{k, Table[Apply[Plus, Table[k*(10^n-1)/9, {n, 1, m}]], {m, 1, 35}]}, {k, 1, 9}]
Table[4/9*Sum[10^i - 1, {i, n}], {n, 18}] (* Robert G. Wilson v, Nov 20 2004 *)

Crossrefs

Cf. A057932, A002275-A002283.

Sequence in context: A264727 A283049 A159903 * A196963 A220325 A265419

Adjacent sequences: A099668 A099669 A099670 * A099672 A099673 A099674

Keyword

base,nonn

Author

Labos Elemer, Nov 17 2004

Status

approved