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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
OFFSET
0,2
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
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