A287837 Number of words over the alphabet {0,1,...,10} such that no two consecutive terms have distance 7.

1, 11, 113, 1163, 11969, 123179, 1267697, 13046507, 134268161, 1381821131, 14221015793, 146355621323, 1506219260609, 15501259470059, 159531252482417, 1641816303234347, 16896756789790721, 173893016807610251, 1789620438445474673, 18417883434877577483

Offset: 0

Author

David Nacin, Jun 07 2017

Keywords

• nonn
• easy

Comments

In general, the number of sequences on {0,1,...,10} such that no two consecutive terms have distance 6+k for k in {0,1,2,3,4} has generating function (-1 - x)/(-1 + 10*x + (2*k+1)*x^2).

Links

• Index entries for linear recurrences with constant coefficients, signature (10,3).

Crossrefs

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

Programs

Mathematica

LinearRecurrence[{10, 3}, {1, 11, 113}, 20]

Python

def a(n):
 if n in [0,1,2]:
  return [1, 11, 113][n]
 return 10*a(n-1) + 3*a(n-2)

Formula

For n>2, a(n) = 10*a(n-1) + 3*a(n-2), a(0)=1, a(1)=11, a(2)=113.

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

a(n) = A015588(n)+A015588(n+1). - R. J. Mathar, Oct 20 2019