A255379 Number of strings of n decimal digits that contain at least one string of exactly 9 consecutive "0" digits.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 18, 261, 3420, 42300, 504000, 5850000, 66600000, 747000000, 8280000000, 90899999991, 989999999757, 10709999995383, 115199999925399, 1232999998904070, 13139999984885400, 139499999800740000, 1475999997460650000, 15569999968482900000

Offset

0,11

Links

Table of n, a(n) for n=0..27.

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

Formula

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

G.f.: x^9*(x-1)^2/((10*x-1)*(9*x^11-9*x^10+10*x-1)). - Alois P. Heinz, Feb 26 2015

Crossrefs

Cf. A255371-A255378 (for the k=1 through k=8 cases of "exactly k consecutive '0' digits"), A255380 (for the k=10 case).

Sequence in context: A255376 A255377 A255378 * A255380 A255381 A078205

Adjacent sequences: A255376 A255377 A255378 * A255380 A255381 A255382

Keyword

nonn,base,easy

Author

Jon E. Schoenfield, Feb 22 2015

Status

approved