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

1, 0, 6, 4, 21, 24, 64, 84, 174, 236, 420, 576, 926, 1260, 1896, 2540, 3639, 4800, 6618, 8592, 11499, 14700, 19200, 24204, 30972, 38544, 48480, 59620, 73884, 89892, 109960, 132480, 160221, 191308, 229038, 271248, 321809, 378264, 445128, 519608, 606954, 704016

Offset

0,3

Comments

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.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,3,-6,-6, 6,13,-2,-18, -2,13,6,-6, -6,3,2,-1)

Formula

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

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

Prog

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

Crossrefs

Column k=6 of A321414.

Cf. A053090, A198808.

Sequence in context: A107983 A009278 A213573 * A185734 A292696 A318209

Adjacent sequences: A321414 A321415 A321416 * A321418 A321419 A321420

Keyword

nonn,easy

Author

Andrew Howroyd, Nov 09 2018

Status

approved