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A136293 Linear bound on the genera of Heegaard splittings of closed, orientable 3-manifolds that admit a generalized triangulation with n generalized tetrahedra. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 19 18:44 EDT 2018. Contains 315210 sequences. (Running on oeis4.)