A198810 Number of closed paths of length n whose steps are 9th roots of unity, U_9(n).

1, 0, 0, 18, 0, 0, 2430, 0, 0, 640080, 0, 0, 215488350, 0, 0, 84569753268, 0, 0, 36905812607664, 0, 0, 17358832115127360, 0, 0, 8632718277709807710, 0, 0, 4482588877386712735500, 0, 0, 2409165357084756621531180, 0, 0, 1331700439352817463265831040

Offset

0,4

Comments

U_9(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.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..200

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

Formula

E.g.f.: ( Sum_{n>=0} x^(3*n)/n!^3 )^3. - Paul D. Hanna, Oct 30 2011

Prog

(PARI) {a(n)=n!*polcoeff(sum(m=0, n, x^(3*m)/m!^3+x*O(x^n))^3, n)} /* Paul D. Hanna, Oct 30 2011 */

Crossrefs

Cf. A006480.

Sequence in context: A008424 A023920 A214359 * A347532 A243911 A289660

Adjacent sequences: A198807 A198808 A198809 * A198811 A198812 A198813

Keyword

nonn

Author

Simon Plouffe, Oct 30 2011

Extensions

Terms a(21) and beyond from Andrew Howroyd, Nov 01 2018

Status

approved