A331456
Number of regions in an equal-armed cross with arms of length n (see Comments for definition).
Original entry on oeis.org
4, 104, 568, 1900, 4808, 10180, 19180, 33132, 53628, 82432, 121448, 172948, 239356, 323168, 427272, 554892, 709476, 893772, 1111588, 1367292, 1664604, 2008240, 2402560, 2852532, 3363280, 3938712, 4585568, 5308720, 6112736, 7006068, 7994412, 9084788, 10281812
Offset: 0
- Lars Blomberg, Table of n, a(n) for n = 0..48
- Scott R. Shannon, Colored illustration for a(0).
- Scott R. Shannon, Colored illustration for a(1).
- Scott R. Shannon, Colored illustration for a(2).
- Scott R. Shannon, Colored illustration for a(3).
- Scott R. Shannon, Colored illustration for a(4).
- Scott R. Shannon, Colored illustration for a(5).
- Scott R. Shannon, Colored illustration for a(9).
- Scott R. Shannon, Colored illustration for a(1) classifying nodes and cells.
- Scott R. Shannon, Colored illustration for a(2) classifying nodes and cells.
- Scott R. Shannon, Colored illustration for a(3) classifying nodes and cells.
- Scott R. Shannon, Colored illustration for a(4) classifying nodes and cells.
- Scott R. Shannon, Colored illustration for a(5) classifying nodes and cells.
- Scott R. Shannon, Colored illustration for a(6) classifying nodes and cells.
- N. J. A. Sloane, Illustration for a(1). (One of the "arms" has been cropped by the scanner, but all four arms are the same.)
- N. J. A. Sloane (in collaboration with Scott R. Shannon), Art and Sequences, Slides of guest lecture in Math 640, Rutgers Univ., Feb 8, 2020. Mentions this sequence.
See
A331455 for a different family of crosses.
A331452 is a similar sequence for a rectangular region;
A007678 for a polygonal region.
A330850
The number of vertices inside a cross with width 3 and height n (see Comments in A331455 for definition) formed by the straight line segments mutually connecting all vertices and all points.
Original entry on oeis.org
45, 69, 119, 219, 357, 575, 871, 1301, 1815, 2543, 3435, 4635, 6023, 7731, 9727, 12259, 15087, 18585, 22543, 27165, 32215, 38239, 44899, 52631, 60979, 70465, 80815, 92749, 105511, 120079, 135867, 153331, 171851, 192311, 214159, 238583, 264323, 292371, 322171
Offset: 2
Corrected offset and a(11) and beyond from
Lars Blomberg, May 31 2020
A333036
Number of edges in an equal-armed cross with arms of length n (see Comments in A331456 for definition).
Original entry on oeis.org
8, 172, 964, 3316, 8524, 18188, 34540, 59908, 97324, 150028, 221692, 316124, 438364, 592364, 784060, 1019468, 1304996, 1644900, 2047412, 2519172, 3068556, 3704004, 4434044, 5265868, 6211652, 7276492, 8474484, 9813996, 11304292, 12958380, 14791124, 16810732
Offset: 0
A333037
Table read by rows: T(n,k) = number of k-sided polygons in an equal-armed cross with arms of length n (see Comments in A331456 for definition) for k = 3,4,5,6,7.
Original entry on oeis.org
4, 0, 0, 0, 0, 84, 20, 0, 0, 0, 380, 180, 0, 8, 0, 1076, 764, 40, 20, 0, 2380, 2316, 64, 48, 0, 4716, 5188, 224, 52, 0, 8236, 10492, 360, 92, 0, 13620, 18772, 632, 108, 0, 21188, 31380, 864, 196, 0, 31596, 49228, 1376, 224, 8, 44980, 74268, 1920, 272, 8
Offset: 0
Table begins:
4, 0, 0, 0, 0
84, 20, 0, 0, 0
380, 180, 0, 8, 0
1076, 764, 40, 20, 0
2380, 2316, 64, 48, 0
4716, 5188, 224, 52, 0
8236, 10492, 360, 92, 0
13620, 18772, 632, 108, 0
21188, 31380, 864, 196, 0
31596, 49228, 1376, 224, 8
44980, 74268, 1920, 272, 8
The row sums are A331456.
A330851
The number of edges inside a cross with width 3 and height n (see Comments in A331455 for definition) formed by the straight line segments mutually connecting all vertices and all points.
Original entry on oeis.org
108, 172, 294, 522, 848, 1352, 2046, 3032, 4260, 5958, 8048, 10806, 14082, 18070, 22778, 28646, 35314, 43436, 52676, 63370, 75290, 89330, 104908, 122816, 142476, 164644, 188954, 216686, 246584, 280386, 317186, 357658, 401138, 448884, 500014, 556706, 617160
Offset: 2
Corrected offset and a(11) and beyond from
Lars Blomberg, May 31 2020
A333459
Number of vertices in an diagonal-edged (or diamond-shaped) checkerboard with width and height 2*n-1 (see Comments in A333434 for definition).
Original entry on oeis.org
5, 69, 785, 4177, 12681, 33601, 71777, 125389, 238801, 379793, 548293, 878397, 1203101, 1673693, 2311477, 3063609, 3934365, 4931077, 6501545, 7873689, 9852941, 12071685, 14067849, 17728005, 20417893, 24047817, 29003717
Offset: 1
Showing 1-6 of 6 results.
Comments