%I #18 May 15 2019 04:53:36

%S 1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,6,6,6,6,

%T 7,7,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,

%U 11,12,12,12,12,12,12,13,13,13,13,13,13,14,14,14,14,14,14,15,15,15,15,15,15

%N Thickness of complete graph K_n.

%C This is the minimal number of planar graphs whose union is K_n.

%H L. W. Beineke, <a href="http://dx.doi.org/10.1016/S0898-1221(97)00214-9">Biplanar graphs: a survey</a>, Computers Math. Applic., 34 (1997), 1-8.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphThickness.html">Graph Thickness</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,1,-1).

%F a(n) = floor((n+7)/6), except a(9) = a(10) = 3.

%F G.f.: (x^16-x^14-x^10+x^8-x^6+x^4+1) / ((x-1)^2*(x+1)*(x^2-x+1)*(x^2+x+1)). - _Colin Barker_, May 08 2014

%t LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4}, 88] (* _Georg Fischer_, May 15 2019 *)

%Y Cf. A124157, A124158, A124159.

%K nonn,easy

%O 1,5

%A _N. J. A. Sloane_, Dec 02 2006