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A287826
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Number of sequences over the alphabet {0,1,...,9} such that no two consecutive terms have distance 2.
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0
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1, 10, 84, 708, 5968, 50308, 424080, 3574860, 30134944, 254028100, 2141377008, 18051134892, 152165391616, 1282706408548, 10812811724688, 91148603152524, 768354066287200, 6476983198439812, 54598931916359472, 460251829451302764, 3879778213203474880
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..20.
Index entries for linear recurrences with constant coefficients, signature (10, -13, -2).
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FORMULA
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a(n) = 10*a(n-1) - 13*a(n-2) - 2a(n-3), a(0)=1, a(1)=10, a(2)=84.
G.f.: (1 - 3 x^2)/(1 - 10 x + 13 x^2 + 2 x^3).
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MATHEMATICA
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LinearRecurrence[{10, -13, -2}, {1, 10, 84}, 40]
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PROG
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(Python)
def a(n):
.if n in [0, 1, 2]:
..return [1, 10, 84][n]
.return 10*a(n-1)-13*a(n-2)-2*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-A287831.
Sequence in context: A090763 A016131 A027310 * A335647 A155593 A239990
Adjacent sequences: A287823 A287824 A287825 * A287827 A287828 A287829
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KEYWORD
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nonn,easy
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AUTHOR
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David Nacin, Jun 02 2017
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STATUS
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approved
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