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

0,6

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).

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

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).

Sequence in context: A365137 A255372 A255373 * A255375 A255376 A255377

Adjacent sequences: A255371 A255372 A255373 * A255375 A255376 A255377

Keyword

nonn,base,easy

Author

Jon E. Schoenfield, Feb 22 2015

Status

approved