A124156 Thickness of complete graph K_n.

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, 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, 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

Offset

1,5

Comments

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

Links

Table of n, a(n) for n=1..88.

L. W. Beineke, Biplanar graphs: a survey, Computers Math. Applic., 34 (1997), 1-8.

Eric Weisstein's World of Mathematics, Graph Thickness

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,1,-1).

Formula

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

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

Mathematica

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 *)

Crossrefs

Cf. A124157, A124158, A124159.

Sequence in context: A029835 A074280 A000523 * A324965 A072749 A066490

Adjacent sequences: A124153 A124154 A124155 * A124157 A124158 A124159

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 02 2006

Status

approved