A287835 Number of words of length n over the alphabet {0,1,...,10} such that no two consecutive terms have distance 4.

1, 11, 107, 1043, 10169, 99149, 966719, 9425675, 91901945, 896059709, 8736735695, 85184670011, 830565128489, 8098152315149, 78958372642847, 769857662314475, 7506244118089817, 73187166301583837, 713587411625345903, 6957599532298617755, 67837787583138657929

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Index entries for linear recurrences with constant coefficients, signature (10,-1,-14)

Formula

For n>3, a(n) = 10*a(n-1) - a(n-2) - 14*a(n-3), a(0)=1, a(1)=11, a(2)=107, a(3)=1043.

G.f.: (1 + x - 2 x^2 - 2 x^3)/(1 - 10 x + x^2 + 14 x^3).

Mathematica

LinearRecurrence[{10, -1, -14}, {1, 11, 107, 1043}, 20]

Prog

(Python)
def a(n):
.if n in [0, 1, 2, 3]:
..return [1, 11, 107, 1043][n]
.return 10*a(n-1) - a(n-2) - 14*a(n-3)

Crossrefs

Cf. A040000, A003945, A083318, A078057, A003946, A126358, A003946, A055099, A003947, A015448, A126473. A287804-A287819. A287825-A287839.

Sequence in context: A140617 A224717 A163413 * A001721 A193308 A080158

Adjacent sequences: A287832 A287833 A287834 * A287836 A287837 A287838

Keyword

nonn,easy

Author

David Nacin, Jun 07 2017

Status

approved