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%I #24 Sep 08 2022 08:45:43
%S 0,0,110,1054,7097,41201,220171,1115862,5451131,25919515,120721773,
%T 553162595,2501388936,11188504443,49589159037,218081007181,
%U 952654230982,4137309942806,17876235129762,76889316253171,329384246847644,1405944884946771,5981601330173431
%N Upper bound arising in Hadwiger's conjecture.
%D 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 .
%H Nathaniel Johnston, <a href="/A159484/b159484.txt">Table of n, a(n) for n = 0..250</a>
%H Hugo Hadwiger, <a href="http://www.ngzh.ch/archiv/1943_88/88_2/88_17.pdf">Über eine Klassifikation der Streckenkomplexe</a>, Vierteljschr. Naturforsch. ges. Zürich 88: 133-143 (1943).
%H A. V. Kostochka, <a href="https://doi.org/10.1007/BF02579141">Lower bound of the Hadwiger number of graphs by their average degree</a>, Combinatorica 4 (4) (1984), 307-316.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Hadwiger_conjecture_(combinatorial_geometry)">Hadwiger conjecture (combinatorial geometry)</a>.
%F a(n) = floor((4^n)*(5*n*log(n))).
%e a(1) = (4^1) * (5 * 1 * log(1)) = 0.
%e a(2) = floor ((4^2) * (5 * 2 * log(2))) = floor(110.903549) = 110.
%e a(3) = floor(1054.6678) = 1054.
%t Table[If[n==0, 0, Floor[(4^n)*(5*n*Log[n])]], {n,0,30}] (* _G. C. Greubel_, Jun 12 2018 *)
%o (PARI) for(n=0, 30, print1(if(n==0, 0, floor((4^n)*(5*n*log(n)))) , ", ")) \\ _G. C. Greubel_, Jun 12 2018
%o (Magma) [0] cat [ Floor((4^n)*(5*n*Log(n))) : n in [1..30]]; // _G. C. Greubel_, Jun 12 2018
%K easy,nonn
%O 0,3
%A _Jonathan Vos Post_, Apr 14 2009
%E a(7)-a(22) from _Nathaniel Johnston_, Apr 26 2011
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