A198802 Number of closed paths of length n whose steps are 18th roots of unity, U_18(n).

1, 0, 18, 36, 918, 5400, 82800, 801360, 10907190, 132053040, 1802041668, 24199809480, 340640607384, 4834708246368, 70229958125184, 1032223723667136, 15391538570569590, 231935110984687968, 3531542904056225916, 54244559313713885688, 839979883121036697468

Offset: 0

Author

Simon Plouffe, Oct 30 2011

Keywords

• nonn

Comments

U_18(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.

Crossrefs

Cf. A002898, A198808.

Programs

PARI

seq(n)={Vec(serlaplace(sum(k=0, n, if(k,2,1)*(x^k*besseli(k, 2*x + O(x^(n-k+1)))/k!)^3)^3))} \\ Andrew Howroyd, Nov 01 2018

Formula

E.g.f.: g(x)^3 where g(x) is the e.g.f. of A002898.

a(n) ~ 2^(n-3) * 3^(2*n + 9/2) / (Pi^3 * n^3). - Vaclav Kotesovec, Apr 30 2024