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 1-3 of 3 results.

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.

A369178 Irregular table read by rows: T(n,k) is the number of k-sided regions, k>=3, 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

2, 8, 4, 22, 14, 52, 34, 98, 82, 184, 146, 302, 268, 484, 426, 8, 710, 694, 4, 1064, 986, 8, 1498, 1436, 12, 2056, 1986, 12, 2710, 2780, 12, 3624, 3630, 24, 4682, 4728, 20, 6012, 5970, 24, 7518, 7628, 28, 9408, 9406, 32, 11526, 11702, 40, 14028, 14246, 64, 16782, 17330, 60
Offset: 1

Views

Author

Scott R. Shannon, Jan 15 2024

Keywords

Comments

Unlike the graph in A306302, or the complete bipartite graph of order n, for n>=8 the graph contains regions with 5 edges. It is likely 5 is the maximum number of edges in any region for all n.

Examples

			The table begins:
2;
8, 4;
22, 14;
52, 34;
98, 82;
184, 146;
302, 268;
484, 426, 8;
710, 694, 4;
1064, 986, 8;
1498, 1436, 12;
2056, 1986, 12;
2710, 2780, 12;
3624, 3630, 24;
4682, 4728, 20;
6012, 5970, 24;
7518, 7628, 28;
9408, 9406, 32;
11526, 11702, 40;
14028, 14246, 64;
16782, 17330, 60;
20220, 20518, 68;
23998, 24468, 80;
28304, 28786, 84;
.
.
		

Crossrefs

Cf. A369175 (regions), A369176 (vertices), A369177 (edges), A306302, A324042, A324043, A368758.

Formula

Sum of row(n) = A369175(n).

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

Views

Author

Scott R. Shannon, Jan 15 2024

Keywords

Comments

See A369175 and A369176 for images of the graph.

Crossrefs

Cf. A369175 (regions), A369176 (vertices), A369178 (k-gons), A306302, A331757, A290132, A368757.

Formula

a(n) = A369175(n) + A369176(n) - 1 by Euler's formula.
Showing 1-3 of 3 results.