A255379 Number of strings of n decimal digits that contain at least one string of exactly 9 consecutive "0" digits.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 18, 261, 3420, 42300, 504000, 5850000, 66600000, 747000000, 8280000000, 90899999991, 989999999757, 10709999995383, 115199999925399, 1232999998904070, 13139999984885400, 139499999800740000, 1475999997460650000, 15569999968482900000

Offset: 0

Author

Jon E. Schoenfield, Feb 22 2015

Keywords

• nonn
• base
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (20,-100,0,0,0,0,0,0,0,-9,99,-90).

Crossrefs

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

Formula

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

G.f.: x^9*(x-1)^2/((10*x-1)*(9*x^11-9*x^10+10*x-1)). - Alois P. Heinz, Feb 26 2015