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A287835
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Number of words of length n over the alphabet {0,1,...,10} such that no two consecutive terms have distance 4.
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0
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1, 11, 107, 1043, 10169, 99149, 966719, 9425675, 91901945, 896059709, 8736735695, 85184670011, 830565128489, 8098152315149, 78958372642847, 769857662314475, 7506244118089817, 73187166301583837, 713587411625345903, 6957599532298617755, 67837787583138657929
(list;
graph;
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listen;
history;
text;
internal format)
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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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For n>3, a(n) = 10*a(n-1) - a(n-2) - 14*a(n-3), a(0)=1, a(1)=11, a(2)=107, a(3)=1043.
G.f.: (1 + x - 2 x^2 - 2 x^3)/(1 - 10 x + x^2 + 14 x^3).
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MATHEMATICA
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LinearRecurrence[{10, -1, -14}, {1, 11, 107, 1043}, 20]
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PROG
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(Python)
def a(n):
.if n in [0, 1, 2, 3]:
..return [1, 11, 107, 1043][n]
.return 10*a(n-1) - a(n-2) - 14*a(n-3)
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CROSSREFS
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Cf. A040000, A003945, A083318, A078057, A003946, A126358, A003946, A055099, A003947, A015448, A126473. A287804-A287819. A287825-A287839.
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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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