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

0,8

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).

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

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 *)

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).

Sequence in context: A255373 A255374 A255375 * A255377 A255378 A255379

Adjacent sequences: A255373 A255374 A255375 * A255377 A255378 A255379

Keyword

nonn,base,easy

Author

Jon E. Schoenfield, Feb 22 2015

Status

approved