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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.)