|
| |
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
| |
|
|
