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

Author

Eric W. Weisstein, Jan 19 2018

Keywords

• nonn
• tabf

Comments

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

Examples

			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
		

Links

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

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).

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).

Extensions

Corrected by Eric W. Weisstein, Mar 28 2019