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
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Apr 29 2018
STATUS
approved