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

0,2

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

Table of n, a(n) for n=0..19.

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

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A142483 A001268 A065538 * A276200 A104096 A239821

Adjacent sequences: A287834 A287835 A287836 * A287838 A287839 A287840

Keyword

nonn,easy

Author

David Nacin, Jun 07 2017

Status

approved