A255377 - OEIS

%I #13 Aug 25 2016 17:19:19

%S 0,0,0,0,0,0,0,1,18,261,3420,42300,504000,5850000,66600000,746999991,

%T 8279999757,90899995383,989999925399,10709998904070,115199984885400,

%U 1232999800740000,13139997460650000,139499968482900081,1475999617032002916,15569995426740068526

%N Number of strings of n decimal digits that contain at least one string of exactly 7 consecutive "0" digits.

%H Alois P. Heinz, <a href="/A255377/b255377.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (20,-100,0,0,0,0,0,-9,99,-90).

%F a(0) = a(1) = ... = a(6) = 0, a(7) = 1, a(n) = 9*(10^(n-8) - a(n-8) + sum_{i=7..n-1} a(i)) for n>=8.

%F G.f.: x^7*(x-1)^2/((10*x-1)*(9*x^9-9*x^8+10*x-1)). - _Alois P. Heinz_, Feb 26 2015

%Y Cf. A255371-A255376 (for the k=1 through k=6 cases of "exactly k consecutive '0' digits"), A255378-A255380 (for the cases k=8 through k=10).

%K nonn,base,easy

%O 0,9

%A _Jon E. Schoenfield_, Feb 22 2015