A298446 Triangle T(n,k) read by rows: number of n-node connected graphs with rectilinear crossing number k (k=0..A014540(n)).

1, 1, 2, 6, 20, 1, 99, 11, 1, 1, 646, 149, 38, 15, 1, 2, 1, 0, 0, 1, 5974, 3008, 1251, 542, 171, 80, 47, 12, 15, 7, 4, 1, 3, 0, 0, 1, 0, 0, 0, 1, 71885

Offset

1,3

Comments

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

T(9,1) >= 71335. - Eric W. Weisstein, Mar 28 2019

Links

Table of n, a(n) for n=1..41.

Eric Weisstein's World of Mathematics, Connected Graph

Eric Weisstein's World of Mathematics, Rectilinear Crossing Number

Formula

T(n,0) = A003094(n).

kmax(n) = A014540(n).

T(n,kmax(n)) = 1 for n > 4.

sum(k=0..kmax(n), T(n,k)) = A001349(n).

Example

Triangle begins:
1
1
2
6
20,1
99,11,1,1
646,149,38,15,1,2,1,0,0,1
5974,3008,1251,542,171,80,47,12,15,7,4,1,3,0,0,1,0,0,0,1

Crossrefs

Cf. A014540 (rectilinear crossing number for K_n).

Cf. A298445 (counts for simple graph).

Sequence in context: A332406 A127942 A110956 * A364563 A357516 A205012

Adjacent sequences: A298443 A298444 A298445 * A298447 A298448 A298449

Keyword

nonn,tabf

Author

Eric W. Weisstein, Jan 19 2018

Extensions

Corrected by Eric W. Weisstein, Mar 28 2019

Status

approved