A287834 Number of words of length n over the alphabet {0,1,...,10} such that no two consecutive terms have distance 3.

1, 11, 105, 1005, 9621, 92105, 881753, 8441329, 80811789, 773639469, 7406320733, 70903294113, 678781988705, 6498216958121, 62209699634757, 595555173609653, 5701457600593525, 54582044135967257, 522532964509030377, 5002390498942001761, 47889630709552579709

Offset: 0

Author

David Nacin, Jun 07 2017

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (10,-2,-21,10).

Crossrefs

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

Programs

Mathematica

LinearRecurrence[{10, -2, -21, 10}, {1, 11, 105, 1005, 9621}, 20]

Python

def a(n):
 if n in [0,1,2,3,4]:
  return [1, 11, 105, 1005, 9621][n]
 return 10*a(n-1) - 2*a(n-2) - 21*a(n-3) + 10*a(n-4)

Formula

a(n) = 10*a(n-1) - 2*a(n-2) - 21*a(n-3) + 10*a(n-4), a(0)=1, a(1)=11, a(2)=105, a(3)=1005, a(4)=9621.

G.f.: (-1 - x + 3*x^2 + 2*x^3 - 2*x^4)/(-1 + 10*x - 2*x^2 - 21*x^3 + 10*x^4).