A255378 Number of strings of n decimal digits that contain at least one string of exactly 8 consecutive "0" digits.

0, 0, 0, 0, 0, 0, 0, 0, 1, 18, 261, 3420, 42300, 504000, 5850000, 66600000, 747000000, 8279999991, 90899999757, 989999995383, 10709999925399, 115199998904070, 1232999984885400, 13139999800740000, 139499997460650000, 1475999968482900000, 15569999617032000081

Offset

0,10

Links

Table of n, a(n) for n=0..26.

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

Formula

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

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

Mathematica

LinearRecurrence[{20, -100, 0, 0, 0, 0, 0, 0, -9, 99, -90}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 18, 261}, 30] (* Harvey P. Dale, Mar 26 2022 *)

Crossrefs

Cf. A255371-A255377 (for the k=1 through k=7 cases of "exactly k consecutive '0' digits"), A255379 and A255380 (for the cases k=9 and k=10).

Sequence in context: A255375 A255376 A255377 * A255379 A255380 A255381

Adjacent sequences: A255375 A255376 A255377 * A255379 A255380 A255381

Keyword

nonn,base,easy

Author

Jon E. Schoenfield, Feb 22 2015

Status

approved