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

0,2

Links

Table of n, a(n) for n=0..20.

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

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).

Mathematica

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

Prog

(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)

Crossrefs

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

Sequence in context: A090763 A016131 A027310 * A335647 A364416 A155593

Adjacent sequences: A287823 A287824 A287825 * A287827 A287828 A287829

Keyword

nonn,easy

Author

David Nacin, Jun 02 2017

Status

approved