A287811 Number of septenary sequences of length n such that no two consecutive terms have distance 5.

1, 7, 45, 291, 1881, 12159, 78597, 508059, 3284145, 21229047, 137226717, 887047443, 5733964809, 37064931183, 239591481525, 1548743682699, 10011236540769, 64713650292711, 418315611378573, 2704034619149571, 17479154549033145, 112987031151647583

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Index entries for linear recurrences with constant coefficients, signature (6, 3).

Formula

a(n) = 6*a(n-1) + 3*a(n-2), a(0)=1, a(1)=7.

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

a(n) = A090018(n-1)+A090018(n). - R. J. Mathar, Oct 20 2019

Example

For n=2 the a(2) = 49-4 = 45 sequences contain every combination except these four: 05, 50, 16, 61.

Mathematica

LinearRecurrence[{6, 3}, {1, 7}, 40]

Prog

(Python)
def a(n):
.if n in [0, 1]:
..return [1, 7][n]
.return 6*a(n-1)-3*a(n-2)

Crossrefs

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

Cf. A287804-A287819.

Sequence in context: A198629 A190973 A099842 * A115194 A062274 A182556

Adjacent sequences: A287808 A287809 A287810 * A287812 A287813 A287814

Keyword

nonn,easy

Author

David Nacin, Jun 01 2017

Status

approved