A136293 Linear bound on the genera of Heegaard splittings of closed, orientable 3-manifolds that admit a generalized triangulation with n generalized tetrahedra.

26, 102, 178, 254, 330, 406, 482, 558, 634, 710, 786, 862, 938, 1014, 1090, 1166, 1242, 1318, 1394, 1470, 1546, 1622, 1698, 1774, 1850, 1926, 2002, 2078, 2154, 2230, 2306, 2382, 2458, 2534, 2610, 2686, 2762, 2838, 2914, 2990, 3066, 3142, 3218, 3294, 3370

Offset

0,1

Comments

Let N be a closed, orientable 3-manifold that admits a triangulation with t tetrahedra. Let F be a Heegaard surface for N. S. Schleimer showed that if g(F) >= 2^{2^{16}t^2}, then the Hempel distance of F (denoted by d(F)) is at most two. In this paper we prove the following generalization:

Let M be an orientable 3-manifold that admits a generalized triangulation with t generalized tetrahedra. Let S be a Heegaard surface for M. If g(S) >= 76t+26, then d(S) <= 2.

Links

Table of n, a(n) for n=0..44.

Tsuyoshi Kobayashi, Yo'av Rieck, A linear bound on the genera of Heegaard splittings with distances greater than two, arXiov:0803.2751 March 20, 2008.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

a(n) = 76*n + 26.

a(n) = 2*a(n-1)-a(n-2). G.f.: 2*(25*x+13)/(x-1)^2. [Colin Barker, Nov 09 2012]

Mathematica

LinearRecurrence[{2, -1}, {26, 102}, 50] (* Harvey P. Dale, Oct 14 2013 *)

Crossrefs

Sequence in context: A159541 A144129 A026915 * A065013 A031434 A173089

Adjacent sequences: A136290 A136291 A136292 * A136294 A136295 A136296

Keyword

easy,nonn

Author

Jonathan Vos Post, Mar 20 2008

Status

approved