

A198800


Number of closed paths of length n whose steps are 20th roots of unity, U_20(n).


2



1, 0, 20, 0, 1140, 480, 102800, 151200, 12310900, 38707200, 1812247920, 9574488000, 313983978000, 2391608419200, 62051403928800, 611744666332800, 13627749414064500, 160896284989440000, 3253345101771050000, 43527416858084016000, 829176006298475046640
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OFFSET

0,3


COMMENTS

U_20(n) (comment in article) : For each m >= 1, the sequence (U_m(N)), N >= 0 is Precursive 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, Reykjav´k, Iceland DMTCS proc. AO, 2011, 599610.


FORMULA

E.g.f.: g(x)^2 where g(x) is the e.g.f. of A070190.  Andrew Howroyd, Nov 01 2018


PROG

(PARI) seq(n)={Vec(serlaplace(sum(k=0, n, if(k, 2, 1)*(x^k*besseli(k, 2*x + O(x^(nk+1)))/k!)^5)^2))} \\ Andrew Howroyd, Nov 01 2018


CROSSREFS

Cf. A070190, A198808.
Sequence in context: A086684 A221335 A298672 * A060430 A040404 A040405
Adjacent sequences: A198797 A198798 A198799 * A198801 A198802 A198803


KEYWORD

nonn


AUTHOR

Simon Plouffe, Oct 30 2011


STATUS

approved



