A287807 Number of senary sequences of length n such that no two consecutive terms have distance 2.

1, 6, 28, 132, 624, 2952, 13968, 66096, 312768, 1480032, 7003584, 33141312, 156826368, 742110336, 3511703808, 16617560832, 78635142144, 372105487872, 1760822074368, 8332299518976, 39428864667648, 186579390892032, 882903157346304, 4177942598725632

Offset

0,2

Links

Table of n, a(n) for n=0..23.

Index entries for linear recurrences with constant coefficients, signature (6, -6).

Formula

For n>2, a(n) = 6*a(n-1) - 6*a(n-2), a(1)=6, a(2)=28.

G.f.: (1 - 2*x^2)/(1 - 6*x + 6*x^2).

Example

For n=2 the a(2)=28=36-8 sequences contain every combination except these eight: 02,20,13,31,24,42,35,53.

Mathematica

LinearRecurrence[{6, -6}, {1, 6, 28}, 40]

Prog

(Python)
def a(n):
.if n in [0, 1, 2]:
..return [1, 6, 28][n]
.return 6*a(n-1)-6*a(n-2)

Crossrefs

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

Sequence in context: A171859 A338584 A084778 * A155588 A368574 A208439

Adjacent sequences: A287804 A287805 A287806 * A287808 A287809 A287810

Keyword

nonn,easy

Author

David Nacin, Jun 01 2017

Status

approved