

A124156


Thickness of complete graph K_n.


1



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
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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), 18.
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^16x^14x^10+x^8x^6+x^4+1) / ((x1)^2*(x+1)*(x^2x+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



