A255374 Number of strings of n decimal digits that contain at least one string of exactly 4 consecutive "0" digits.

0, 0, 0, 0, 1, 18, 261, 3420, 42300, 503991, 5849757, 66595383, 746925399, 8278904070, 90884885481, 989800742916, 10707460718526, 115168484215116, 1232617054343121, 13135427089598511, 139446180653268195, 1475374347592901460, 15562803326717545290

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,-9,99,-90).

Crossrefs

Cf. A255371-A255373 (for the k=1 through k=3 cases of "exactly k consecutive '0' digits"), A255375-A255380 (for the cases k=5 through k=10).

Formula

a(0) = a(1) = a(2) = a(3) = 0, a(4) = 1, a(n) = 9*(10^(n-5) - a(n-5) + sum_{i=4..n-1} a(i)) for n>=5.

G.f.: x^4*(x-1)^2/((10*x-1)*(9*x^6-9*x^5+10*x-1)). - Alois P. Heinz, Feb 26 2015