A326289 a(0) = 0, a(n) = 2^binomial(n,2) - 2^(n - 1).

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.

Links

Table of n, a(n) for n=0..16.

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}]

Crossrefs

Cf. A000088, A000108, A002662, A006125, A016098, A054726, A324170.

Cf. A326210, A326244, A326248, A326250, A326257, A326279, A326290.

Sequence in context: A298555 A240298 A298383 * A369534 A078533 A299302

Adjacent sequences: A326286 A326287 A326288 * A326290 A326291 A326292

Keyword

nonn

Author

Gus Wiseman, Jun 23 2019

Status

approved