

A129033


Number of nnode triangulations of the torus S_1 in which every node has degree >= 6.


0



0, 1, 1, 2, 1, 1, 4, 2, 2, 4, 5, 2, 5, 3, 6, 6, 4, 3, 11, 5, 5, 7, 9, 4, 11, 5, 11, 8, 7, 8, 16, 6, 8, 10, 16, 6, 15, 7, 13, 14, 10, 7, 24, 10, 14, 12, 16, 8, 19, 12, 21, 14, 13, 9, 30, 10, 14, 19, 23, 14, 23, 11, 20, 16, 23, 11, 36, 12, 17, 22, 23, 16, 27, 13, 34, 21, 19, 13, 40, 18, 20, 20, 31, 14, 39, 20, 27, 22, 22, 20, 47, 16, 27, 27, 37
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OFFSET

6,4


LINKS

Table of n, a(n) for n=6..100.
Ulrich Brehm and Wolfgang Kuhnel, Equivelar maps on the torus, Universitat Stuttgart, 2006.
M. Jungerman and G. Ringel, Minimal triangulations on orientable surfaces, Acta Math. 145 (1980), 121154.
Thom Sulanke, Generating triangulations of surfaces (surftri), (also subpages).
Thom Sulanke and Frank H. Lutz, Isomorphismfree lexicographic enumeration of triangulated surfaces and 3manifolds, arXiv:math/0610022 [math.CO], 20062007.


MATHEMATICA

T2[n_] := Piecewise[{{DivisorSigma[0, n]  2  T6[n], Mod[n, 2] == 1}, {DivisorSigma[0, n/2]  2, Mod[n, 4] == 2}}, DivisorSigma[0, n/2] + DivisorSigma[0, n/4]  4  T6[n]];
T3[n_] := Length[{ToRules[Reduce[n == p^2 + p q + q^2 && 0 < q < p, {p, q}, Integers]]}];
T6[n_] := Boole[n >= 9 && (IntegerQ[Sqrt[n]]  IntegerQ[Sqrt[n/3]])]
T[n_] := Piecewise[{{DivisorSigma[1, n]/6 + T2[n]/2 + 2/3 T3[n] +
5/6 T6[n]  (2  Mod[n, 2]), n > 6}}];
Table[T[n], {n, 7, 100}] (* Eric W. Weisstein after Brehm and Kuhnel, Aug 30 2018 *)


CROSSREFS

Sequence in context: A244581 A064191 A127420 * A054090 A239456 A122517
Adjacent sequences: A129030 A129031 A129032 * A129034 A129035 A129036


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, May 12 2007


EXTENSIONS

Terms a(18) and beyond from Thom Sulanke added by Ed Pegg Jr, Aug 30 2018


STATUS

approved



