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A303732 Number of noncrossing path sets on n nodes up to rotation with each path having a prime number of nodes. 6
1, 0, 1, 1, 1, 7, 8, 45, 96, 258, 1260, 2511, 12594, 35799, 126043, 482640, 1487929, 6012740, 20051360, 74529198, 276148256, 977824914, 3744986184, 13527623583, 50997301218, 190934525258, 711190503929, 2707743977818, 10155615925523, 38691707792278 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..500

PROG

(PARI) \\ number of path sets with restricted path lengths

NCPathSetsModCyclic(v)={ my(n=#v);

my(p=serreverse(x/(1 + x*v[1] + sum(k=2, #v, (k*2^(k-3))*x^k*v[k])) + O(x^2*x^n) )/x);

my(vars=variables(p));

my(h=substvec(p + O(x^(n\2+1)), vars, apply(t->t^2, vars)));

my(q=x*deriv(p)/p);

my(Q=sum(i=1, #v\2, v[2*i]*2^(i-1)*(x^2*h)^i));

1 + Q/2 + intformal((p - 1 + sum(d=2, n, eulerphi(d)*substvec(q + O(x^(n\d+1)), vars, apply(t->t^d, vars))))/x)

}

Vec(NCPathSetsModCyclic(vector(30, k, isprime(k))))

CROSSREFS

Cf. A303729, A303731.

Sequence in context: A037953 A296636 A041106 * A119453 A047192 A270009

Adjacent sequences:  A303729 A303730 A303731 * A303733 A303734 A303735

KEYWORD

nonn

AUTHOR

Andrew Howroyd, Apr 29 2018

STATUS

approved

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Last modified July 18 11:30 EDT 2019. Contains 325138 sequences. (Running on oeis4.)