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A277836 Number of '6' digits 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, ...).

%I A277836 #20 Jan 01 2021 11:53:06
%S A277836 0,0,1,22,343,4664,58986,713315,8367717,96022849,1083685281,
%T A277836 12071420713,133059886145,1454055651577,15775124417009,
%U A277836 170096923182441,1824426021947881,19478828120713394,207133960219479637,2194796392318253180,23182531824417099723
%N A277836 Number of '6' digits 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, ...).
%H A277836 David A. Corneth, <a href="/A277836/b277836.txt">Table of n, a(n) for n = 0..998</a>
%F A277836 a(n) = A277839(n) =  A083449(n) = A277830(n) - 1 for n < 6,
%F A277836 a(n) = A277835(n) - 7*10^(n-6) for n >= 6,
%F A277836 a(n) = A277837(n) + 8*10^(n-7) for n >= 7.
%e A277836 For n=2 there is only one digit '6' in the sequence 0, 1, 2, ..., 12.
%e A277836 For n=3 there are 11 + 10 = 21 more digits '6' in { 16, 26, ..., 56, 60, ..., 69, 76, 86, ..., 116 }, where 66 accounts for two '6's.
%t A277836 T[int_Integer, {bndsLow_Integer, bndsUpp_Integer}] := Table[
%t A277836    Count[
%t A277836     Flatten[Table[
%t A277836       IntegerDigits[m],
%t A277836       {m, 1, Sum[
%t A277836          10^i - 1,
%t A277836          {i, n}
%t A277836          ]/9
%t A277836        }
%t A277836       ]],
%t A277836     int
%t A277836     ],
%t A277836    {n, bndsLow, bndsUpp}
%t A277836    ];
%t A277836 T[6, {0, 7}](* _Robert P. P. McKone_, Jan 01 2021 *)
%o A277836 (PARI) print1(c=N=0);for(n=1,8,print1(","c+=sum(k=N+1,N=N*10+n,#select(d->d==6,digits(k)))))
%o A277836 (PARI) A277836(n,m=6)=if(n>m,A277836(n,m+1)+(m+2)*10^(n-m-1),A277830(n)-(m>n)) \\ _M. F. Hasler_, Nov 02 2016
%Y A277836 Cf. A277830 - A277838, A277849, A277635, A272525, A083449, A014824.
%K A277836 nonn,base
%O A277836 0,4
%A A277836 _M. F. Hasler_, Nov 01 2016
%E A277836 More terms from _Lars Blomberg_, Nov 05 2016
%E A277836 Removed incorrect b-file. - _David A. Corneth_, Dec 31 2020