A287816 Number of nonary sequences of length n such that no two consecutive terms have distance 1.

1, 9, 65, 471, 3413, 24733, 179233, 1298853, 9412437, 68209395, 494295113, 3582023557, 25957960001, 188110345129, 1363185009337, 9878634630295, 71587804656589, 518777540353453, 3759441118026705, 27243657291488469, 197427447142906157, 1430703538380753875

Offset: 0

Author

David Nacin, Jun 02 2017

Keywords

• nonn
• easy

Examples

			For n=2 the a(2) = 81 - 16 = 65 sequences contain every combination except these sixteen: 01,10,12,21,23,32,34,43,45,54,56,65,67,76,78,87.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (9, -11, -15, 19, 1).

Crossrefs

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

Programs

Mathematica

LinearRecurrence[{9, -11, -15, 19, 1}, {1, 9, 65 , 471, 3413}, 40]

Python

def a(n):
 if n in [0, 1, 2, 3, 4]:
  return [1, 9, 65 , 471, 3413][n]
 return 9*a(n-1)-11*a(n-2)-15*a(n-3)+19*a(n-4)+a(n-5)

Formula

a(n) = 9*a(n-1) - 11*a(n-2) - 15*a(n-3) + 19*a(n-4) + a(n-5), a(0)=1, a(1)=9, a(2)=65, a(3)=471, a(4)=3413.

G.f: (-1 + 5 x^2 - 5 x^4)/(-1 + 9 x - 11 x^2 - 15 x^3 + 19 x^4 + x^5).