A303732 Number of noncrossing path sets on n nodes up to rotation with each path having a prime number of nodes.

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

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 A342611

Adjacent sequences: A303729 A303730 A303731 * A303733 A303734 A303735

Keyword

nonn

Author

Andrew Howroyd, Apr 29 2018

Status

approved