A255377 Number of strings of n decimal digits that contain at least one string of exactly 7 consecutive "0" digits.

0, 0, 0, 0, 0, 0, 0, 1, 18, 261, 3420, 42300, 504000, 5850000, 66600000, 746999991, 8279999757, 90899995383, 989999925399, 10709998904070, 115199984885400, 1232999800740000, 13139997460650000, 139499968482900081, 1475999617032002916, 15569995426740068526

Offset

0,9

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

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

Formula

a(0) = a(1) = ... = a(6) = 0, a(7) = 1, a(n) = 9*(10^(n-8) - a(n-8) + sum_{i=7..n-1} a(i)) for n>=8.

G.f.: x^7*(x-1)^2/((10*x-1)*(9*x^9-9*x^8+10*x-1)). - Alois P. Heinz, Feb 26 2015

Crossrefs

Cf. A255371-A255376 (for the k=1 through k=6 cases of "exactly k consecutive '0' digits"), A255378-A255380 (for the cases k=8 through k=10).

Sequence in context: A255374 A255375 A255376 * A255378 A255379 A255380

Adjacent sequences: A255374 A255375 A255376 * A255378 A255379 A255380

Keyword

nonn,base,easy

Author

Jon E. Schoenfield, Feb 22 2015

Status

approved