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A321417 Number of n element multisets of the 12th roots of unity with zero sum. 2


%S 1,0,6,4,21,24,64,84,174,236,420,576,926,1260,1896,2540,3639,4800,

%T 6618,8592,11499,14700,19200,24204,30972,38544,48480,59620,73884,

%U 89892,109960,132480,160221,191308,229038,271248,321809,378264,445128,519608,606954,704016

%N Number of n element multisets of the 12th roots of unity with zero sum.

%C Equivalently, the number of closed convex paths of length n whose steps are the 12th roots of unity up to translation. For even n, there will be 6 paths of zero area consisting of n/2 steps in one direction followed by n/2 steps in the opposite direction.

%H Andrew Howroyd, <a href="/A321417/b321417.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,-6,-6, 6,13,-2,-18, -2,13,6,-6, -6,3,2,-1)

%F G.f.: ((2/(1 - x^3) - 1)/(1 - x^2)^3)^2.

%F G.f.: (1 - x + x^2)^2/((1 + x + x^2)^2*(1 - x)^8*(1 + x)^4).

%o (PARI) Vec(((2/(1 - x^3) - 1)/(1 - x^2)^3)^2 + O(x^40))

%Y Column k=6 of A321414.

%Y Cf. A053090, A198808.

%K nonn,easy

%O 0,3

%A _Andrew Howroyd_, Nov 09 2018

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Last modified April 20 06:31 EDT 2021. Contains 343121 sequences. (Running on oeis4.)