A368755
Number of regions in the hyperoctahedral (or cocktail party) graph of order n.
Original entry on oeis.org
0, 2, 18, 64, 186, 380, 838, 1504, 2242, 4082, 6266, 8320, 13010, 17866, 20218, 31808, 41390, 50100, 66530, 82560, 93446, 123642, 149398, 171920, 212166, 249810, 283678, 340704, 394882, 428892, 521406, 594560, 659382, 764866, 863154, 954192, 1086490, 1212506, 1326654, 1498720, 1660278
Offset: 1
A368756
Number of vertices in the hyperoctahedral (or cocktail party) graph of order n.
Original entry on oeis.org
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
- 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.
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.
Original entry on oeis.org
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
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;
.
.
A368815
Number of edges in a regular 2n-gon when all vertices are connect by straight lines except for the n lines joining diametrically opposite vertices.
Original entry on oeis.org
0, 4, 24, 104, 320, 648, 1540, 2832, 3996, 7860, 12100, 15552, 25376, 35084, 36840, 62752, 81600, 97272, 131556, 163720, 178332, 245564, 296516, 336960, 421600, 497172, 557280, 678552, 786016, 836520, 1038500, 1185344, 1301124, 1525444, 1720740, 1893600, 2166720, 2419612, 2628600, 2991440
Offset: 1
A369177
Number of edges in a graph of n adjacent rectangles in a row with all possible diagonals drawn, as in A306302, but without the rectangles' edges which are perpendicular to the row.
Original entry on oeis.org
6, 24, 66, 152, 318, 576, 998, 1608, 2474, 3600, 5162, 7100, 9670, 12772, 16546, 21036, 26622, 33024, 40814, 49716, 60006, 71560, 85158, 100264, 117626, 136780, 158358, 182080, 209106, 238312, 271314, 307304, 346866, 389488, 436286, 486444, 542026, 601436, 665814, 734504, 809882, 889544
Offset: 1
Showing 1-5 of 5 results.
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