A321418 -id:A321418 - cp's OEIS frontend

A321419 Number of n element multisets of the 30th roots of unity with zero sum.

1, 0, 15, 10, 120, 156, 760, 1350, 4350, 8770, 22896, 47610, 110110, 226260, 483180, 964696

Offset: 0

Andrew Howroyd, Nov 09 2018

Equivalently, the number of closed convex paths of length n whose steps are the 30th roots of unity up to translation. For even n, there will be 15 paths of zero area consisting of n/2 steps in one direction followed by n/2 steps in the opposite direction.

Column k=15 of A321414.

Cf. A321418.

A198805 Number of closed paths of length n whose steps are 15th roots of unity, U_15(n).

Original entry on oeis.org

1, 0, 0, 30, 0, 360, 7650, 0, 302400, 4544400, 11226600, 324324000, 4310633250, 24324300000, 437404968000, 5634178329780, 45972927000000, 697866761592000, 8962716395833200, 88725951057744000, 1258898645656852200

Offset: 0

Simon Plouffe, Oct 30 2011

nonn

U_15(n), (comment in article): For each m >= 1, the sequence (U_m(N)), N >= 0 is P-recursive but is not algebraic when m > 2.

Gilbert Labelle and Annie Lacasse, Closed paths whose steps are roots of unity, in FPSAC 2011, Reykjavik, Iceland DMTCS proc. AO, 2011, 599-610.

Cf. A198808, A321418.

cp's OEIS Frontend

A321419 Number of n element multisets of the 30th roots of unity with zero sum.

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