A368756 Number of vertices in the hyperoctahedral (or cocktail party) graph of order n.

2, 5, 17, 49, 151, 273, 693, 1249, 1711, 3525, 5529, 6777, 11711, 16133, 15937, 29121, 38227, 44561, 61985, 77041, 81423, 116165, 140997, 157649, 201211, 237125, 263449, 324689, 377359, 392185, 499789, 570241, 621255, 735493, 831537, 909097, 1048887, 1171013, 1265501, 1450081, 1608523

Offset

1,1

Links

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

Scott R. Shannon, Image for n = 2.

Scott R. Shannon, Image for n = 3.

Scott R. Shannon, Image for n = 4.

Scott R. Shannon, Image for n = 5.

Scott R. Shannon, Image for n = 6.

Scott R. Shannon, Image for n = 9.

Scott R. Shannon, Image for n = 10.

Scott R. Shannon, Image for n = 15. Note this 30-gon still contains vertices with 7 chords crossing, so this maximum possible value is the same as the regular n-gon with all diagonals drawn; see A007569.

Eric Weisstein's World of Mathematics, Cocktail Party Graph.

Formula

a(n) = A368757(n) - A368755(n) + 1 by Euler's formula.

Crossrefs

Cf. A368755 (regions), A368757 (edges), A368758 (k-gons), A007569, A129348, A193130, A282010.

Sequence in context: A219554 A074494 A051438 * A148401 A148402 A148403

Adjacent sequences: A368753 A368754 A368755 * A368757 A368758 A368759

Keyword

nonn

Author

Scott R. Shannon, Jan 04 2024

Status

approved