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A292350
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Number of Lyndon words (aperiodic necklaces) with 6 beads of n colors.
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2
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0, 9, 116, 670, 2580, 7735, 19544, 43596, 88440, 166485, 295020, 497354, 804076, 1254435, 1897840, 2795480, 4022064, 5667681, 7839780, 10665270, 14292740, 18894799, 24670536, 31848100, 40687400, 51482925, 64566684, 80311266, 99133020, 121495355, 147912160
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = (n^6 - n^3 - n^2 + n)/6.
G.f.: x^2*(9 + 53*x + 47*x^2 + 11*x^3) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)
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PROG
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(PARI) concat(0, Vec(x^2*(9 + 53*x + 47*x^2 + 11*x^3) / (1 - x)^7 + O(x^40))) \\ Colin Barker, Dec 08 2017
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CROSSREFS
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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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