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A099676 Partial sums of repdigits of A002283. 2
9, 108, 1107, 11106, 111105, 1111104, 11111103, 111111102, 1111111101, 11111111100, 111111111099, 1111111111098, 11111111111097, 111111111111096, 1111111111111095, 11111111111111094, 111111111111111093, 1111111111111111092, 11111111111111111091 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) is the maximal positive integer k such that the sequence 1, 2, 3, 4, ..., k-1, k has a total of n*k digits. - Bui Quang Tuan, Mar 12 2015

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

FORMULA

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

From Colin Barker, Mar 12 2014: (Start)

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

G.f.: -9*x / ((x-1)^2*(10*x-1)). (End)

EXAMPLE

9 + 99 + 999 + 9999 + 99999 = a(5) = 111105.

MAPLE

a:=n->sum((10^(n-j)-1^(n-j)), j=0..n): seq(a(n), n=1..17); # Zerinvary Lajos, Jan 15 2007

MATHEMATICA

<<NumberTheory`NumberTheoryFunctions` Table[{k, Table[Apply[Plus, Table[k*(10^n-1)/9, {n, 1, m}]], {m, 1, 35}]}, {k, 1, 9}]

CoefficientList[Series[-9/((x - 1)^2 (10 x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Mar 14 2014 *)

LinearRecurrence[{12, -21, 10}, {9, 108, 1107}, 20] (* Harvey P. Dale, Apr 18 2015 *)

PROG

(Sage) [gaussian_binomial(n, 1, 10)-n for n in xrange(2, 19)] # Zerinvary Lajos, May 29 2009

(PARI) Vec(-9*x/((x-1)^2*(10*x-1)) + O(x^100)) \\ Colin Barker, Mar 12 2014

(MAGMA) [(10/9)*(10^n-1)-n: n in [1..20]]; // Vincenzo Librandi, Mar 14 2014

CROSSREFS

Cf. A057932, A002275-A002283, A099669-A099674.

Sequence in context: A249048 A080505 A104224 * A268839 A214668 A234467

Adjacent sequences:  A099673 A099674 A099675 * A099677 A099678 A099679

KEYWORD

base,nonn,easy

AUTHOR

Labos Elemer, Nov 17 2004

STATUS

approved

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Last modified September 20 12:42 EDT 2018. Contains 315239 sequences. (Running on oeis4.)