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A287811
Number of septenary sequences of length n such that no two consecutive terms have distance 5.
1
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
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)
KEYWORD
nonn,easy
AUTHOR
David Nacin, Jun 01 2017
STATUS
approved