This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A255375 #19 Dec 12 2023 15:46:12
%S A255375 0,0,0,0,0,1,18,261,3420,42300,504000,5849991,66599757,746995383,
%T A255375 8279925399,90898904070,989984885400,10709800740081,115197460652916,
%U A255375 1232968482968526,13139617033315116,139495426762343121,1475946175849599240,15569374280153300271
%N A255375 Number of strings of n decimal digits that contain at least one string of exactly 5 consecutive "0" digits.
%H A255375 Alois P. Heinz, <a href="/A255375/b255375.txt">Table of n, a(n) for n = 0..1000</a>
%H A255375 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (20,-100,0,0,0,-9,99,-90).
%F A255375 a(0) = a(1) = ... = a(4) = 0, a(5) = 1, a(n) = 9*(10^(n-6) - a(n-6) + sum_{i=5..n-1} a(i)) for n>=6.
%F A255375 G.f.: x^5*(x-1)^2/((10*x-1)*(9*x^7-9*x^6+10*x-1)). - _Alois P. Heinz_, Feb 26 2015
%t A255375 LinearRecurrence[{20,-100,0,0,0,-9,99,-90},{0,0,0,0,0,1,18,261},30] (* _Harvey P. Dale_, Dec 12 2023 *)
%Y A255375 Cf. A255371-A255374 (for the k=1 through k=4 cases of "exactly k consecutive '0' digits"), A255376-A255380 (for the cases k=6 through k=10).
%K A255375 nonn,base,easy
%O A255375 0,7
%A A255375 _Jon E. Schoenfield_, Feb 22 2015