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A287833
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Number of words of length n over the alphabet {0,1,...,10} such that no two consecutive terms have distance 2.
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0
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1, 11, 103, 967, 9079, 85243, 800351, 7514541, 70554457, 662439857, 6219685951, 58396989455, 548292695881, 5147951686649, 48334414751849, 453814602701801, 4260891430727991, 40005754941255473, 375616336261903907, 3526683405274793053, 33112233522155404139
(list;
graph;
refs;
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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a(n) = 10*a(n-1) - 2*a(n-2) - 37*a(n-3) + 16*a(n-4) + 19*a(n-5) + a(n-6), a(0)=1, a(1)=11, a(2)=103, a(3)=967, a(4)=9079, a(5)=85243.
G.f.: (-1 - x + 5*x^2 + 4*x^3 - 6*x^4 - 3*x^5)/(-1 + 10*x - 2*x^2 - 37*x^3 + 16*x^4 + 19*x^5 + x^6).
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MATHEMATICA
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LinearRecurrence[{10, -2, -37, 16, 19, 1}, {1, 11, 103, 967, 9079, 85243}, 20]
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PROG
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(Python)
def a(n):
.if n in [0, 1, 2, 3, 4, 5]:
..return [1, 11, 103, 967, 9079, 85243][n]
.return 10*a(n-1) - 2*a(n-2) - 37*a(n-3) + 16*a(n-4) + 19*a(n-5) + a(n-6)
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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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