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A103456
a(n) = 0^n + 10^n - 1.
2
1, 9, 99, 999, 9999, 99999, 999999, 9999999, 99999999, 999999999, 9999999999, 99999999999, 999999999999, 9999999999999, 99999999999999, 999999999999999, 9999999999999999, 99999999999999999, 999999999999999999
OFFSET
0,2
COMMENTS
A transform of 10^n under the matrix A103452.
Except for n = 0, the same as A002283. - Felix Fröhlich, Jun 22 2021
FORMULA
G.f.: (1 - 2*x + 10*x^2)/((1 - x)*(1 - 10*x));
a(n) = Sum_{k = 0..n} A103452(n, k)*10^k;
a(n) = Sum_{k = 0..n} (2*0^(n-k) - 1)*0^(k*(n-k))*10^k.
a(n) = A002283(n), n > 0. - R. J. Mathar, Aug 30 2008
E.g.f.: 1 - exp(x) + exp(10*x). - G. C. Greubel, Jun 21 2021
MATHEMATICA
Table[Boole[n==0] + 10^n -1, {n, 0, 40}] (* Alonso del Arte, Nov 03 2019 *)
PROG
(Magma) [1] cat [10^n -1: n in [1..40]]; // G. C. Greubel, Jun 21 2021
(Sage) [1]+[10^n -1 for n in (1..40)] # G. C. Greubel, Jun 21 2021
(PARI) a(n) = 0^n + 10^n - 1 \\ Felix Fröhlich, Jun 22 2021
(PARI) Vec((1 - 2*x + 10*x^2)/((1 - x)*(1 - 10*x)) + O(x^20)) \\ Felix Fröhlich, Jun 22 2021
CROSSREFS
Sequence in context: A242809 A108908 A116260 * A002283 A155157 A264005
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Feb 06 2005
STATUS
approved