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 A292350 Number of Lyndon words (aperiodic necklaces) with 6 beads of n colors. 2

%I

%S 0,9,116,670,2580,7735,19544,43596,88440,166485,295020,497354,804076,

%T 1254435,1897840,2795480,4022064,5667681,7839780,10665270,14292740,

%U 18894799,24670536,31848100,40687400,51482925,64566684,80311266,99133020,121495355,147912160

%N Number of Lyndon words (aperiodic necklaces) with 6 beads of n colors.

%H Colin Barker, <a href="/A292350/b292350.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7, -21, 35, -35, 21, -7, 1).

%F a(n) = (n^6 - n^3 - n^2 + n)/6.

%F From _Colin Barker_, Dec 08 2017: (Start)

%F G.f.: x^2*(9 + 53*x + 47*x^2 + 11*x^3) / (1 - x)^7.

%F 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.

%F (End)

%o (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

%Y Row n=6 of A074650.

%K nonn,easy

%O 1,2

%A _Eric M. Schmidt_, Dec 08 2017

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Last modified September 23 04:54 EDT 2020. Contains 337295 sequences. (Running on oeis4.)