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A094797 Number of times 1 is used in writing out all numbers 1 through 10^n. 0
1, 2, 21, 301, 4001, 50001, 600001, 7000001, 80000001, 900000001, 10000000001, 110000000001, 1200000000001, 13000000000001, 140000000000001, 1500000000000001, 16000000000000001, 170000000000000001, 1800000000000000001, 19000000000000000001 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) = n*10^(n-1) + 1.
a(n) = 21*a(n-1)-120*a(n-2)+100*a(n-3). - Colin Barker, May 23 2014
G.f.: -(99*x^2-19*x+1) / ((x-1)*(10*x-1)^2). - Colin Barker, May 23 2014
a(n) = A094798(A011557(n)). - Michel Marcus, Oct 03 2023
MATHEMATICA
Table[ n*10^(n - 1) + 1, {n, 0, 17}] (* Robert G. Wilson v, Jun 15 2004 *)
LinearRecurrence[{21, -120, 100}, {1, 2, 21}, 20] (* Harvey P. Dale, Sep 07 2022 *)
PROG
(PARI) Vec(-(99*x^2-19*x+1)/((x-1)*(10*x-1)^2) + O(x^100)) \\ Colin Barker, May 23 2014
CROSSREFS
Sequence in context: A266969 A229036 A097627 * A359918 A234525 A230382
KEYWORD
base,nonn,easy
AUTHOR
Lekraj Beedassy, Jun 11 2004
EXTENSIONS
More terms from Robert G. Wilson v, Jun 15 2004
Further terms from Colin Barker, May 23 2014
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)