A255376 Number of strings of n decimal digits that contain at least one string of exactly 6 consecutive "0" digits.

0, 0, 0, 0, 0, 0, 1, 18, 261, 3420, 42300, 504000, 5850000, 66599991, 746999757, 8279995383, 90899925399, 989998904070, 10709984885400, 115199800740000, 1232997460650081, 13139968482902916, 139499617032068526, 1475995426741315116, 15569946175522343121

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,-9,99,-90).

Crossrefs

Cf. A255371-A255375 (for the k=1 through k=5 cases of "exactly k consecutive '0' digits"), A255377-A255380 (for the cases k=7 through k=10).

Programs

Mathematica

LinearRecurrence[{20,-100,0,0,0,0,-9,99,-90},{0,0,0,0,0,0,1,18,261},30] (* Harvey P. Dale, Aug 17 2021 *)

Formula

a(0) = a(1) = ... = a(5) = 0, a(6) = 1, a(n) = 9*(10^(n-7) - a(n-7) + sum_{i=6..n-1} a(i)) for n>=7.

G.f.: x^6*(x-1)^2/((10*x-1)*(9*x^8-9*x^7+10*x-1)). - Alois P. Heinz, Feb 26 2015