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A287811
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Number of septenary sequences of length n such that no two consecutive terms have distance 5.
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1
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1, 7, 45, 291, 1881, 12159, 78597, 508059, 3284145, 21229047, 137226717, 887047443, 5733964809, 37064931183, 239591481525, 1548743682699, 10011236540769, 64713650292711, 418315611378573, 2704034619149571, 17479154549033145, 112987031151647583
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OFFSET
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0,2
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LINKS
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FORMULA
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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).
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EXAMPLE
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For n=2 the a(2) = 49-4 = 45 sequences contain every combination except these four: 05, 50, 16, 61.
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MATHEMATICA
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LinearRecurrence[{6, 3}, {1, 7}, 40]
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PROG
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(Python)
def a(n):
.if n in [0, 1]:
..return [1, 7][n]
.return 6*a(n-1)-3*a(n-2)
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CROSSREFS
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Cf. A040000, A003945, A083318, A078057, A003946, A126358, A003946, A055099, A003947, A015448, A126473.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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