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A298445 Triangle T(n,k) read by rows: number of n-node 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 3 22:32 EST 2021. Contains 349468 sequences. (Running on oeis4.)