

A298445


Triangle T(n,k) read by rows: number of nnode simple graphs with rectilinear crossing number k (k=0..A014540(n)).


1



1, 2, 4, 11, 33, 1, 142, 12, 1, 1, 822, 162, 39, 16, 1, 2, 1, 0, 0, 1, 6966, 3183, 1291, 559, 172, 82, 48, 12, 15, 8, 4, 1, 3, 0, 0, 1, 0, 0, 0, 1, 79853
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OFFSET

1,2


COMMENTS

Computed up to n=8 using data provided by Geoffrey Exoo. (There appear to be some problems with n=9 data.)


LINKS

Table of n, a(n) for n=1..41.
Eric Weisstein's World of Mathematics, Rectilinear Crossing Number
Eric Weisstein's World of Mathematics, Simple Graph


FORMULA

T(n,0) = A005470(n).
T(n,1) = A307071(n).
kmax(n) = A014540(n).
T(n,kmax(n)) = 1 for n > 4.
Sum_{k=0..kmax(n)} T(n,k) = A000088(n).


EXAMPLE

Triangle begins:
1
2
4
11
33, 1
142, 12, 1, 1
822, 162, 39, 16, 1, 2, 1, 0, 0, 1
6966, 3183, 1291, 559, 172, 82, 48, 12, 15, 8, 4, 1, 3, 0, 0, 1, 0, 0, 0, 1


CROSSREFS

Cf. A014540 (rectilinear crossing number for K_n).
Cf. A298446 (counts for simple connected graphs).
Cf. A307071 (number of simple graphs with crossing number 1).
Sequence in context: A123449 A123404 A178925 * A294224 A296270 A123439
Adjacent sequences: A298442 A298443 A298444 * A298446 A298447 A298448


KEYWORD

nonn,tabf


AUTHOR

Eric W. Weisstein, Jan 19 2018


EXTENSIONS

Corrected by Eric W. Weisstein, Mar 28 2019


STATUS

approved



