%I
%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
