A287806 Number of senary sequences of length n such that no two consecutive terms have distance 1.

1, 6, 26, 114, 500, 2194, 9628, 42252, 185422, 813722, 3571010, 15671340, 68773514, 301811860, 1324498252, 5812546998, 25508302906, 111942925778, 491260382084, 2155891150146, 9461106209228, 41519967599596, 182209952129086, 799626506818554, 3509152727035810

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (5, -2, -3).

Formula

For n>3, a(n) = 5*a(n-1) - 2*a(n-2) - 3*a(n-3), a(1)=6, a(2)=26, a(3)=114.

G.f.: (1 + x - 2*x^2 - x^3)/(1 - 5*x + 2*x^2 + 3*x^3).

Example

For n=2 the a(2)=26=36-10 sequences contain every combination except these ten: 01,10,12,21,23,32,34,43,45,54.

Mathematica

LinearRecurrence[{5, -2, -3}, {1, 6, 26, 114}, 40]

Prog

(Python)
def a(n):
.if n in [0, 1, 2, 3]:
..return [1, 6, 26, 114][n]
.return 5*a(n-1)-2*a(n-2)-3*a(n-3)

Crossrefs

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

Sequence in context: A145374 A289789 A124465 * A164549 A283341 A046647

Adjacent sequences: A287803 A287804 A287805 * A287807 A287808 A287809

Keyword

nonn,easy

Author

David Nacin, Jun 01 2017

Status

approved