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A321417 Number of n element multisets of the 12th roots of unity with zero sum. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 6 04:14 EST 2021. Contains 341841 sequences. (Running on oeis4.)