A129115 Number of unrooted unlabeled not necessarily connected triangular maps on a compact closed oriented surface with 2n faces (and thus 3n edges).

1, 3, 17, 124, 1618, 33564, 956263, 33736198, 1402665692, 66902717187, 3596481426812, 215049652739982, 14154852098315796, 1016911004448831247, 79174846391508487198, 6640511488761139957873, 596865894849670793348763, 57234563024075319273338452, 5832189914390355126473955563

Offset: 0

Author

Samuel A. Vidal, Mar 30 2007

Keywords

• nonn

Comments

Equivalently, the number of pair of permutations (sigma,tau) up to simultaneous conjugacy on a set of size 6*n with sigma^3=tau^2=1 with no fixed point.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..300

Crossrefs

Not necessarily connected version of A129114.

Unrooted, not necessarily connected version of A062980.

Cf. also A121350, A121352, A005133.

Programs

PARI

D(m,k)={my(g=gcd(m,k)); sumdiv(g, d, my(j=m/d); x^j*eulerphi(d)*k^(j-1)/j)}
seq(n)={my(t=6*n); Vec(prod(k=1, t, my(A=O(x^(t\k+1)), p=serconvol(exp(A + D(3,k)), exp(A + D(2,k)))); sum(r=0, t\k, if(k*r%6==0, r!*polcoef(p,r)/(k^r)*x^(k*r/6)), O(x*x^n)) ))} \\ Andrew Howroyd, Jan 29 2025

Formula

Euler transform of A129114. - Andrew Howroyd, Jan 29 2025

Extensions

a(17) onwards from Andrew Howroyd, Jan 28 2025