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%I #52 Dec 29 2020 16:51:06
%S 1,1,2,23,344,4665,58986,713307,8367628,96021949,1083676272,
%T 12071330614,133058985146,1454046641578,15775034317010,
%U 170096022182442,1824417011947874,19478738020713306,207133059219478738,2194787382318244170,23182441724417009624,244170096256515775267
%N 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, ...).
%C The first 10 terms are given by a simple explicit formula and linear recurrence, which does not hold for n > 9. Note that A007908 (concat(1..n)) differs from A014824 (a(n) = a(n-1)*10 + n) for n > 9. - _M. F. Hasler_, Nov 07 2020
%H M. F. Hasler, <a href="/A277830/b277830.txt">Table of n, a(n) for n = 0..100</a>
%F a(n) = A083449(n) + 1 for n <= 9.
%F a(n) = 1 + A061217(A014824(n)), taking A061217(0)=0. - _Kevin Ryde_, Nov 07 2020
%o (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.
%o (PARI) apply( A277830(n)={A061217(A014824(n)+!n)+1}, [0..22]) \\ Thanks to Kevin Ryde's formula. - _M. F. Hasler_, Nov 07 2020
%Y Cf. A277831 - A277838, A277849, A277635, A272525, A083449, A014824.
%K nonn,base,easy
%O 0,3
%A _M. F. Hasler_, Nov 01 2016
%E Incorrect data, b-file, links, formulas and programs deleted by _M. F. Hasler_, following observations by _Kevin Ryde_, Nov 07 2020
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