A307071 -id:A307071 - cp's OEIS frontend

A298445 Triangle T(n,k) read by rows: number of n-node simple graphs with rectilinear crossing number k (k=0..A014540(n)).

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

Offset: 1

Eric W. Weisstein, Jan 19 2018

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

			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

Eric Weisstein's World of Mathematics, Rectilinear Crossing Number
Eric Weisstein's World of Mathematics, Simple Graph

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).

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).

Corrected by Eric W. Weisstein, Mar 28 2019

A307072 Number of simple connected graphs on n nodes with crossing number 1.

Original entry on oeis.org

0, 0, 0, 0, 1, 11, 149, 3008, 71335, 1814021

Offset: 1

Eric W. Weisstein, Mar 22 2019

			5-node: K_5.
6-node: includes K_{1,2,3}, (5-1)-lollipop, 2 X 3 queen, utility graph K_{3,3}.

Cf. A307071 (not necessarily connected graphs).

Cf. A003094 (connected graphs with crossing number 0).

a(9) from Eric W. Weisstein, Apr 17 2019

a(10) from Eric W. Weisstein, Apr 28 2019

cp's OEIS Frontend

A298445 Triangle T(n,k) read by rows: number of n-node simple graphs with rectilinear crossing number k (k=0..A014540(n)).

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