A287836 Number of words over the alphabet {0,1,...,10} such that no two consecutive terms have distance 5.

1, 11, 109, 1081, 10721, 106329, 1054553, 10458881, 103729441, 1028771337, 10203182953, 101193470929, 1003620008177, 9953736259545, 98719500126905, 979083577381409, 9710388021269185, 96306012787788969, 955147011506293513, 9472989143467878769, 93951530216004879761

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (10,1,-18).

Formula

For n>3, a(n) = 10*a(n-1) + a(n-2) - 18*a(n-3), a(0)=1, a(1)=11, a(2)=109, a(3)=1081.

G.f.: (1 + x - 2*x^2 - 2*x^3)/(1 - 10*x - x^2 + 18*x^3).

Mathematica

LinearRecurrence[{10, 1, -18}, {1, 11, 109, 1081}, 20]

Prog

(Python)
def a(n):
.if n in [0, 1, 2, 3]:
..return [1, 11, 109, 1081][n]
.return 10*a(n-1) + a(n-2) - 18*a(n-3)

Crossrefs

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

Sequence in context: A165149 A048346 A054320 * A124290 A094703 A324355

Adjacent sequences: A287833 A287834 A287835 * A287837 A287838 A287839

Keyword

nonn,easy

Author

David Nacin, Jun 07 2017

Status

approved