A159484 Upper bound arising in Hadwiger's conjecture.

0, 0, 110, 1054, 7097, 41201, 220171, 1115862, 5451131, 25919515, 120721773, 553162595, 2501388936, 11188504443, 49589159037, 218081007181, 952654230982, 4137309942806, 17876235129762, 76889316253171, 329384246847644, 1405944884946771, 5981601330173431

Offset

0,3

References

Brass, Peter; Moser, William; Pach, Janos (2005), "3.3 Levi-Hadwiger Covering Problem and Illumination", Research Problems in Discrete Geometry, Springer-Verlag, pp. 136-142 .

Links

Nathaniel Johnston, Table of n, a(n) for n = 0..250

Hugo Hadwiger, Über eine Klassifikation der Streckenkomplexe, Vierteljschr. Naturforsch. ges. Zürich 88: 133-143 (1943).

A. V. Kostochka, Lower bound of the Hadwiger number of graphs by their average degree, Combinatorica 4 (4) (1984), 307-316.

Wikipedia, Hadwiger conjecture (combinatorial geometry).

Formula

a(n) = floor((4^n)*(5*n*log(n))).

Example

a(1) = (4^1) * (5 * 1 * log(1)) = 0.
a(2) = floor ((4^2) * (5 * 2 * log(2))) = floor(110.903549) = 110.
a(3) = floor(1054.6678) = 1054.

Mathematica

Table[If[n==0, 0, Floor[(4^n)*(5*n*Log[n])]], {n, 0, 30}] (* G. C. Greubel, Jun 12 2018 *)

Prog

(PARI) for(n=0, 30, print1(if(n==0, 0, floor((4^n)*(5*n*log(n)))) , ", ")) \\ G. C. Greubel, Jun 12 2018
(Magma) [0] cat [ Floor((4^n)*(5*n*Log(n))) : n in [1..30]]; // G. C. Greubel, Jun 12 2018

Crossrefs

Sequence in context: A234760 A234753 A205610 * A283219 A283137 A213087

Adjacent sequences: A159481 A159482 A159483 * A159485 A159486 A159487

Keyword

easy,nonn

Author

Jonathan Vos Post, Apr 14 2009

Extensions

a(7)-a(22) from Nathaniel Johnston, Apr 26 2011

Status

approved