A326289 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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