A287826 Number of sequences over the alphabet {0,1,...,9} such that no two consecutive terms have distance 2.

1, 10, 84, 708, 5968, 50308, 424080, 3574860, 30134944, 254028100, 2141377008, 18051134892, 152165391616, 1282706408548, 10812811724688, 91148603152524, 768354066287200, 6476983198439812, 54598931916359472, 460251829451302764, 3879778213203474880

Offset: 0

Author

David Nacin, Jun 02 2017

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (10, -13, -2).

Crossrefs

Cf. A040000, A003945, A083318, A078057, A003946, A126358, A003946, A055099, A003947, A015448, A126473. A287804-A287819. A287825-A287831.

Programs

Mathematica

LinearRecurrence[{10, -13, -2}, {1, 10, 84}, 40]

Python

def a(n):
 if n in [0, 1, 2]:
  return [1, 10, 84][n]
 return 10*a(n-1)-13*a(n-2)-2*a(n-3)

Formula

a(n) = 10*a(n-1) - 13*a(n-2) - 2a(n-3), a(0)=1, a(1)=10, a(2)=84.

G.f.: (1 - 3 x^2)/(1 - 10 x + 13 x^2 + 2 x^3).