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A255380 Number of strings of n decimal digits that contain at least one string of exactly 10 consecutive "0" digits.

%I A255380 #16 Dec 27 2021 18:02:52
%S A255380 0,0,0,0,0,0,0,0,0,0,1,18,261,3420,42300,504000,5850000,66600000,
%T A255380 747000000,8280000000,90900000000,989999999991,10709999999757,
%U A255380 115199999995383,1232999999925399,13139999998904070,139499999984885400,1475999999800740000
%N A255380 Number of strings of n decimal digits that contain at least one string of exactly 10 consecutive "0" digits.
%H A255380 Colin Barker, <a href="/A255380/b255380.txt">Table of n, a(n) for n = 0..1000</a>
%H A255380 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (20,-100,0,0,0,0,0,0,0,0,-9,99,-90).
%F A255380 a(0) = a(1) = ... = a(9) = 0, a(10) = 1, a(n) = 9*(10^(n-11) - a(n-11) + sum_{i=10..n-1} a(i)) for n>=11.
%F A255380 G.f.: x^10*(x-1)^2/((10*x-1)*(9*x^12-9*x^11+10*x-1)). - _Alois P. Heinz_, Feb 26 2015
%t A255380 CoefficientList[Series[x^10(x-1)^2/((10x-1)(9x^12-9x^11+10x-1)),{x,0,40}],x] (* or *) LinearRecurrence[{20,-100,0,0,0,0,0,0,0,0,-9,99,-90},{0,0,0,0,0,0,0,0,0,0,1,18,261},40] (* _Harvey P. Dale_, Dec 27 2021 *)
%o A255380 (PARI) concat([0,0,0,0,0,0,0,0,0,0], Vec(x^10*(x-1)^2/((10*x-1)*(9*x^12-9*x^11+10*x-1)) + O(x^100))) \\ _Colin Barker_, Feb 27 2015
%Y A255380 Cf. A255371-A255379 (for the k=1 through k=9 cases of "exactly k consecutive '0' digits").
%K A255380 nonn,base,easy
%O A255380 0,12
%A A255380 _Jon E. Schoenfield_, Feb 22 2015