cp's OEIS Frontend

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.

Showing 1-5 of 5 results.

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

Views

Author

Scott R. Shannon, Jan 04 2024

Keywords

Crossrefs

Cf. A368756 (vertices), A368757 (edges), A368758 (k-gons), A129348, A193130, A282010.

Formula

a(n) = A368757(n) - A368756(n) + 1 by Euler's formula.

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

Views

Author

Scott R. Shannon, Jan 04 2024

Keywords

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;
.
.
		

Crossrefs

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

Formula

Sum of row n = A368755(n).

A368757 Number of edges in the hyperoctahedral (or cocktail party) graph of order n.

Original entry on oeis.org

0, 6, 34, 112, 336, 652, 1530, 2752, 3952, 7606, 11794, 15096, 24720, 33998, 36154, 60928, 79616, 94660, 128514, 159600, 174868, 239806, 290394, 329568, 413376, 486934, 547126, 665392, 772240, 821076, 1021194, 1164800, 1280636, 1500358, 1694690, 1863288, 2135376, 2383518, 2592154
Offset: 1

Views

Author

Scott R. Shannon, Jan 04 2024

Keywords

Comments

See A368755 and A368756 for images of the graphs.

Crossrefs

Cf. A368755 (regions), A368756 (vertices), A368758 (k-gons), A129348, A193130, A282010.

Formula

a(n) = A368755(n) + A368756(n) - 1 by Euler's formula.

A368814 Number of vertices 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

2, 4, 12, 48, 150, 288, 728, 1344, 1782, 3780, 5852, 7224, 12350, 17108, 16620, 30720, 40018, 46728, 64676, 80560, 84462, 121044, 146280, 163728, 208250, 245700, 271836, 335664, 389006, 404400, 514352, 587264, 638022, 756228, 853300, 933480, 1074998, 1200724, 1295112, 1485120, 1645002
Offset: 1

Views

Author

Scott R. Shannon, Jan 06 2024

Keywords

Crossrefs

Cf. A368813 (regions), A368815 (edges), A368816 (k-gons), A368756, A007569.

Formula

a(n) = A368815(n) - A368813(n) + 1 by Euler's formula.

A369176 Number of vertices 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

5, 13, 31, 67, 139, 247, 429, 691, 1067, 1543, 2217, 3047, 4169, 5495, 7117, 9031, 11449, 14179, 17547, 21379, 25835, 30755, 36613, 43091, 50605, 58775, 68035, 78171, 89831, 102335, 116593, 132079, 149181, 167391, 187497, 208983, 232977, 258351, 285957, 315323, 347777, 381867, 419371
Offset: 1

Views

Author

Scott R. Shannon, Jan 15 2024

Keywords

Crossrefs

Cf. A369175 (regions), A369177 (edges), A369178 (k-gons), A306302, A331755, A368756.

Formula

a(n) = A369177(n) - A369175(n) + 1 by Euler's formula.
Showing 1-5 of 5 results.