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 A321415 Number of n element multisets of the 2n-th roots of unity with zero sum. 2
 0, 2, 2, 10, 2, 64, 2, 330, 1028, 2010, 2, 24216, 2, 77528, 964696, 490314, 2, 11437750, 2, 21390330 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Equivalently, the number of closed convex paths of length n whose steps are the 2n-th roots of unity up to translation. For even n, there will be n paths of zero area consisting of n/2 steps in one direction followed by n/2 steps in the opposite direction. Compared with A262181, this sequence counts all rotations distinctly and also for even n includes n/2 flat polygons as described above. For prime n, a(n) is always 2. For odd prime the two solutions are the one consisting of all n-th roots of unity and the other consisting of their negated values. LINKS FORMULA a(p) = 2 for prime p. EXAMPLE a(4) = 12 because there are 3 basic shapes illustrated below which with rotations of multiples of 45 degrees give 4 + 2 + 4 = 10 distinct convex paths. o---o o---o o===o===o | | \ \ o---o o---o CROSSREFS Main diagonal of A321414. Cf. A262181, A292355. Sequence in context: A133631 A137450 A344998 * A319692 A308693 A339481 Adjacent sequences: A321412 A321413 A321414 * A321416 A321417 A321418 KEYWORD nonn,more AUTHOR Andrew Howroyd, Nov 08 2018 STATUS approved

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Last modified February 4 05:49 EST 2023. Contains 360046 sequences. (Running on oeis4.)