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A099676
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Partial sums of repdigits of A002283.
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2
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9, 108, 1107, 11106, 111105, 1111104, 11111103, 111111102, 1111111101, 11111111100, 111111111099, 1111111111098, 11111111111097, 111111111111096, 1111111111111095, 11111111111111094, 111111111111111093, 1111111111111111092, 11111111111111111091
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (12,-21,10).
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FORMULA
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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)
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EXAMPLE
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9 + 99 + 999 + 9999 + 99999 = a(5) = 111105.
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MAPLE
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a:=n->sum((10^(n-j)-1^(n-j)), j=0..n): seq(a(n), n=1..17); # Zerinvary Lajos, Jan 15 2007
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MATHEMATICA
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<<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 *)
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PROG
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(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
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CROSSREFS
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Cf. A057932, A002275-A002283, A099669-A099674.
Sequence in context: A249048 A080505 A104224 * A214668 A234467 A166907
Adjacent sequences: A099673 A099674 A099675 * A099677 A099678 A099679
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KEYWORD
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base,nonn,easy
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AUTHOR
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Labos Elemer, Nov 17 2004
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STATUS
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approved
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