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

0,2

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

Formula

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

Prog

(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

Crossrefs

Not necessarily connected version of A129114.

Unrooted, not necessarily connected version of A062980.

Cf. also A121350, A121352, A005133.

Sequence in context: A216314 A330803 A267736 * A246963 A093460 A187613

Adjacent sequences: A129112 A129113 A129114 * A129116 A129117 A129118

Keyword

nonn,changed

Author

Samuel A. Vidal, Mar 30 2007

Extensions

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

Status

approved