A255377 Number of strings of n decimal digits that contain at least one string of exactly 7 consecutive "0" digits.

0, 0, 0, 0, 0, 0, 0, 1, 18, 261, 3420, 42300, 504000, 5850000, 66600000, 746999991, 8279999757, 90899995383, 989999925399, 10709998904070, 115199984885400, 1232999800740000, 13139997460650000, 139499968482900081, 1475999617032002916, 15569995426740068526

Offset: 0

Author

Jon E. Schoenfield, Feb 22 2015

Keywords

• nonn
• base
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (20,-100,0,0,0,0,0,-9,99,-90).

Crossrefs

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).

Formula

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.

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