login
A326289
a(0) = 0, a(n) = 2^binomial(n,2) - 2^(n - 1).
2
0, 0, 0, 4, 56, 1008, 32736, 2097088, 268435328, 68719476480, 35184372088320, 36028797018962944, 73786976294838204416, 302231454903657293672448, 2475880078570760549798240256, 40564819207303340847894502555648, 1329227995784915872903807060280311808
OFFSET
0,4
COMMENTS
Number of simple graphs with vertices {1..n} containing two edges {a,b}, {c,d} that are weakly crossing, meaning a <= c < b <= d or c <= a < d <= b.
EXAMPLE
The a(4) = 56 weakly crossing edge-sets:
{12,13} {12,13,14} {12,13,14,23} {12,13,14,23,24} {12,13,14,23,24,34}
{12,14} {12,13,23} {12,13,14,24} {12,13,14,23,34}
{12,23} {12,13,24} {12,13,14,34} {12,13,14,24,34}
{12,24} {12,13,34} {12,13,23,24} {12,13,23,24,34}
{12,34} {12,14,23} {12,13,23,34} {12,14,23,24,34}
{13,14} {12,14,24} {12,13,24,34} {13,14,23,24,34}
{13,23} {12,14,34} {12,14,23,24}
{13,24} {12,23,24} {12,14,23,34}
{13,34} {12,23,34} {12,14,24,34}
{14,24} {12,24,34} {12,23,24,34}
{14,34} {13,14,23} {13,14,23,24}
{23,24} {13,14,24} {13,14,23,34}
{23,34} {13,14,34} {13,14,24,34}
{24,34} {13,23,24} {13,23,24,34}
{13,23,34} {14,23,24,34}
{13,24,34}
{14,23,24}
{14,23,34}
{14,24,34}
{23,24,34}
MATHEMATICA
Table[If[n==0, 0, 2^Binomial[n, 2]-2^(n-1)], {n, 0, 5}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 23 2019
STATUS
approved