A368758 Irregular table read by rows: T(n,k) is the number of k-sided regions, k>=3, in the hyperoctahedral (or cocktail party) graph of order n.

0, 2, 14, 2, 2, 42, 22, 100, 72, 12, 2, 234, 142, 4, 418, 320, 90, 10, 734, 610, 116, 44, 1248, 878, 82, 20, 14, 1968, 1454, 534, 98, 12, 16, 2696, 2662, 744, 74, 56, 34, 4040, 3434, 770, 74, 0, 2, 5806, 4722, 1932, 430, 94, 26, 7706, 7102, 2048, 894, 92, 24, 10868, 7492, 1448, 406, 4

Offset: 1

Author

Scott R. Shannon, Jan 04 2024

Keywords

• nonn
• tabf

Comments

See A368755 and A368756 for further images of the graphs.

Examples

			The table begins:
0;
2;
14, 2, 2;
42, 22;
100, 72, 12, 2;
234, 142, 4;
418, 320, 90, 10;
734, 610, 116, 44;
1248, 878, 82, 20, 14;
1968, 1454, 534, 98, 12, 16;
2696, 2662, 744, 74, 56, 34;
4040, 3434, 770, 74, 0, 2;
5806, 4722, 1932, 430, 94, 26;
7706, 7102, 2048, 894, 92, 24;
10868, 7492, 1448, 406, 4;
13438, 12122, 4682, 1356, 206, 4;
17438, 15950, 5420, 2194, 296, 84, 6, 2;
22990, 17734, 7166, 1976, 182, 52;
27284, 25902, 9672, 2718, 772, 182;
34160, 31164, 12650, 3710, 648, 188, 0, 0, 8, 32;
.
.
		

Links

• Scott R. Shannon, Image for T(8,k).
• Eric Weisstein's World of Mathematics, Cocktail Party Graph.

Crossrefs

Cf. A368755 (regions), A368756 (vertices), A368757 (edges), A129348, A193130, A282010.

Formula

Sum of row n = A368755(n).