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

Author

David Nacin, Jun 07 2017

Keywords

• nonn
• easy

Links

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

Crossrefs

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

Programs

Mathematica

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

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)

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).