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A303731 Number of noncrossing path sets on n nodes up to rotation and reflection with each path having a prime number of nodes. 6
1, 0, 1, 1, 1, 5, 6, 27, 53, 140, 649, 1297, 6355, 18038, 63226, 241741, 744711, 3008107, 10028056, 37270169, 138083464, 488933323, 1872525356, 6763888465, 25498771059, 95467533318, 355595703773, 1353873044078, 5077809606803, 19345857682140, 73533468653115 (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

NCPathSetsModDihedral(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(R=v[1]*x + sum(i=1, (#v-1)\2, v[2*i+1]*2^(i-1)*x*(x^2*h)^i), Q=sum(i=1, #v\2, v[2*i]*2^(i-1)*(x^2*h)^i), T=intformal((p - 1 + sum(d=2, n, eulerphi(d)*substvec(q + O(x^(n\d+1)), vars, apply(t->t^d, vars))))/x));

O(x*x^n) + (1 + T + (1 + Q + (1+R)^2*h/(1-Q) + v[2]*x^2*h)/2)/2;

}

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

CROSSREFS

Cf. A303729, A303732.

Sequence in context: A022163 A048060 A320665 * A298175 A298144 A115761

Adjacent sequences:  A303728 A303729 A303730 * A303732 A303733 A303734

KEYWORD

nonn

AUTHOR

Andrew Howroyd, Apr 29 2018

STATUS

approved

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Last modified June 25 09:48 EDT 2019. Contains 324347 sequences. (Running on oeis4.)