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A277830 Number of digits '0' in the set of all numbers from 0 to A014824(n) = Sum_{i=1..n} i*10^(n-i) = (0, 1, 12, 123, 1234, 12345, ...). 11
1, 1, 2, 23, 344, 4665, 58986, 713307, 8367628, 96021949, 1083676270, 12071330591, 133058984912, 1454046639233, 15775034293554, 170096021947875, 1824417009602196, 19478737997256517, 207133058984910838, 2194787379972565159, 23182441700960219480 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Colin Barker, Table of n, a(n) for n = 0..990

Index entries for linear recurrences with constant coefficients, signature (22,-141,220,-100).

FORMULA

a(n) = A083449(n) + 1 for n <= 9.

From Colin Barker, Nov 04 2016: (Start)

a(n) = 22*a(n-1)-141*a(n-2)+220*a(n-3)-100*a(n-4) for n>3.

G.f.: (1-21*x+121*x^2-100*x^3) / ((1-x)^2*(1-10*x)^2).

(End)

MATHEMATICA

LinearRecurrence[{22, -141, 220, -100}, {1, 1, 2, 23}, 30] (* Harvey P. Dale, Apr 22 2018 *)

PROG

(PARI) print1(c=1); N=0; for(n=1, 8, print1(", "c+=sum(k=N+1, N=N*10+n, #select(d->d==0, digits(k))))) \\ For purpose of illustration.

(PARI) A277830(n)=(9*n-11)*(10^n+1)\729+2 \\ M. F. Hasler, Nov 02 2016

(PARI) Vec((1-21*x+121*x^2-100*x^3)/((1-x)^2*(1-10*x)^2) + O(x^30)) \\ Colin Barker, Nov 04 2016

CROSSREFS

Cf. A277831 - A277838, A277849, A277635, A272525, A083449, A014824.

Sequence in context: A091693 A276025 A211925 * A197740 A234868 A239109

Adjacent sequences:  A277827 A277828 A277829 * A277831 A277832 A277833

KEYWORD

nonn,base,easy

AUTHOR

M. F. Hasler, Nov 01 2016

STATUS

approved

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Last modified October 16 21:10 EDT 2019. Contains 328103 sequences. (Running on oeis4.)