This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A368756 #18 Feb 16 2025 08:34:06 %S A368756 2,5,17,49,151,273,693,1249,1711,3525,5529,6777,11711,16133,15937, %T A368756 29121,38227,44561,61985,77041,81423,116165,140997,157649,201211, %U A368756 237125,263449,324689,377359,392185,499789,570241,621255,735493,831537,909097,1048887,1171013,1265501,1450081,1608523 %N A368756 Number of vertices in the hyperoctahedral (or cocktail party) graph of order n. %H A368756 Scott R. Shannon, <a href="/A368756/a368756.png">Image for n = 2</a>. %H A368756 Scott R. Shannon, <a href="/A368756/a368756_1.png">Image for n = 3</a>. %H A368756 Scott R. Shannon, <a href="/A368756/a368756_2.png">Image for n = 4</a>. %H A368756 Scott R. Shannon, <a href="/A368756/a368756_3.png">Image for n = 5</a>. %H A368756 Scott R. Shannon, <a href="/A368756/a368756_4.png">Image for n = 6</a>. %H A368756 Scott R. Shannon, <a href="/A368756/a368756_5.png">Image for n = 9</a>. %H A368756 Scott R. Shannon, <a href="/A368756/a368756_6.png">Image for n = 10</a>. %H A368756 Scott R. Shannon, <a href="/A368756/a368756_7.png">Image for n = 15</a>. 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. %H A368756 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CocktailPartyGraph.html">Cocktail Party Graph</a>. %F A368756 a(n) = A368757(n) - A368755(n) + 1 by Euler's formula. %Y A368756 Cf. A368755 (regions), A368757 (edges), A368758 (k-gons), A007569, A129348, A193130, A282010. %K A368756 nonn %O A368756 1,1 %A A368756 _Scott R. Shannon_, Jan 04 2024