A287809 Number of septenary sequences of length n such that no two consecutive terms have distance 2.

1, 7, 39, 219, 1231, 6921, 38913, 218789, 1230147, 6916539, 38888455, 218651553, 1229375193, 6912200477, 38864063403, 218514412227, 1228604118319, 6907865088537, 38839687552689, 218377358251349, 1227833528067027, 6903532420748427, 38815326992539159

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Index entries for linear recurrences with constant coefficients, signature (6, 0, -13, 6).

Formula

For n>4, a(n) = 6*a(n-1) - 13*a(n-3) + 6*a(n-4), a(1)=7, a(2)=39, a(3)=219, a(4)=1231.

G.f.: (1 + x - 3*x^2 - 2*x^3 + 2*x^4)/(1 - 6*x + 13*x^3 - 6*x^4).

Example

For n=2 the a(2)=49-10=39 sequences contain every combination except these ten: 02,20,13,31,24,42,35,53,46,64.

Mathematica

LinearRecurrence[{6, 0, -13, 6}, {1, 7, 39, 219, 1231}, 40]

Prog

(Python)
def a(n):
.if n in [0, 1, 2, 3, 4]:
..return [1, 7, 39, 219, 1231][n]
.return 6*a(n-1)-13*a(n-3)+6*a(n-4)

Crossrefs

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

Sequence in context: A092923 A164550 A125786 * A155589 A071082 A122884

Adjacent sequences: A287806 A287807 A287808 * A287810 A287811 A287812

Keyword

nonn,easy

Author

David Nacin, Jun 01 2017

Status

approved