A333294
Main diagonal of triangle in A333282.
Original entry on oeis.org
4, 56, 624, 3288, 16912, 51864, 164692, 422792, 1023416, 2101272, 4387296, 8214688, 15485996
Offset: 1
A333519
Number of regions in a polygon whose boundary consists of n+2 equally spaced points around a semicircle and n+2 equally spaced points along the diameter (a total of 2n+2 points). See Comments for precise definition.
Original entry on oeis.org
0, 2, 13, 48, 141, 312, 652, 1160, 1978, 3106, 4775, 6826, 9803, 13328, 17904, 23536, 30652, 38640, 48945, 60300, 74248, 89892, 108768, 128990, 153826, 180206, 211483, 245000, 284375, 325140, 374450, 425312, 484168, 545938, 616981, 690132, 775077, 862220
Offset: 0
A333283
Triangle read by rows: T(m,n) (m >= n >= 1) = number of edges formed by drawing the line segments connecting any two of the (m+1) X (n+1) lattice points in an m X n grid of squares and extending them to the boundary of the grid.
Original entry on oeis.org
8, 28, 92, 80, 320, 1028, 178, 716, 2348, 5512, 372, 1604, 5332, 12676, 28552, 654, 2834, 9404, 22238, 49928, 87540, 1124, 5008, 16696, 39496, 88540, 156504, 279100, 1782, 7874, 26458, 62818, 141386, 251136, 447870
Offset: 1
Triangle begins:
8,
28, 92,
80, 320, 1028,
178, 716, 2348, 5512,
372, 1604, 5332, 12676, 28552,
654, 2834, 9404, 22238, 49928, 87540,
1124, 5008, 16696, 39496, 88540, 156504, 279100,
1782, 7874, 26458, 62818, 141386, 251136, 447870, ...
...
T(7,7) corrected Mar 19 2020
- Seppo Mustonen, Statistical accuracy of geometric constructions, 2008.
- Seppo Mustonen, Statistical accuracy of geometric constructions, 2008 [Local copy]
- Seppo Mustonen, On lines and their intersection points in a rectangular grid of points, 2009
- Seppo Mustonen, On lines and their intersection points in a rectangular grid of points, 2009 [Local copy]
- Seppo Mustonen, On lines going through a given number of points in a rectangular grid of points, 2010
- Seppo Mustonen, On lines going through a given number of points in a rectangular grid of points, 2010 [Local copy]
- N. J. A. Sloane, Illustration of T(3,2) = 320. [Black lines correspond to A331454(3,2), black + red lines correspond to A333278(3,2), and black + red + blue lines to T(3,2)]
- N. J. A. Sloane, Illustration of T(3,3) = 1028 [Black lines correspond to A288187(3,3), and black + red lines to T(3,3)]
A333284
Triangle read by rows: T(m,n) (m >= n >= 1) = number of vertices formed by drawing the line segments connecting any two of the (m+1) X (n+1) lattice points in an m X n grid of squares and extending them to the boundary of the grid.
Original entry on oeis.org
5, 13, 37, 35, 129, 405, 75, 289, 933, 2225, 159, 663, 2155, 5157, 11641, 275, 1163, 3793, 9051, 20341, 35677, 477, 2069, 6771, 16129, 36173, 63987, 114409, 755, 3251, 10727, 25635, 57759, 102845, 183961
Offset: 1
Triangle begins:
5,
13, 37,
35, 129, 405,
75, 289, 933, 2225,
159, 663, 2155, 5157, 11641,
275, 1163, 3793, 9051, 20341, 35677,
477, 2069, 6771, 16129, 36173, 63987, 114409,
755, 3251, 10727, 25635, 57759, 102845, 183961, ...
...
T(7,7) corrected Mar 19 2020
- Lars Blomberg, Scott R. Shannon, N. J. A. Sloane, Graphical Enumeration and Stained Glass Windows, 1: Rectangular Grids, (2021). Also arXiv:2009.07918.
- Seppo Mustonen, Statistical accuracy of geometric constructions, 2008.
- Seppo Mustonen, Statistical accuracy of geometric constructions, 2008 [Local copy]
- Seppo Mustonen, On lines and their intersection points in a rectangular grid of points, 2009
- Seppo Mustonen, On lines and their intersection points in a rectangular grid of points, 2009 [Local copy]
- Seppo Mustonen, On lines going through a given number of points in a rectangular grid of points, 2010
- Seppo Mustonen, On lines going through a given number of points in a rectangular grid of points, 2010 [Local copy]
- N. J. A. Sloane, Illustration of T(3,2) = 129. [Black lines correspond to A331453(3,2), black + red lines correspond to A288180(3,2), and black + red + blue lines to T(3,2)]
- N. J. A. Sloane, Illustration of T(3,3) = 405 [Black lines correspond to A288180(3,3), and black + red lines to T(3,3)]
A333285
The main diagonal of the triangular array A333284.
Original entry on oeis.org
5, 37, 405, 2225, 11641, 35677, 114409, 295701, 718469, 1475709, 3093025, 5771929, 10895273, 18785841, 31414269, 50274501, 81288641, 124066161, 190860537, 282399889, 411505049, 580614301, 824814797, 1138709849, 1570665877, 2115178249, 2833746309, 3732420861, 4937226173
Offset: 1
- Lars Blomberg, Scott R. Shannon, N. J. A. Sloane, Graphical Enumeration and Stained Glass Windows, 1: Rectangular Grids, (2021). Also arXiv:2009.07918.
- Seppo Mustonen, Statistical accuracy of geometric constructions, September 02, 2008.
- Seppo Mustonen, Statistical accuracy of geometric constructions, 2008 [Local copy]
- Seppo Mustonen, On lines and their intersection points in a rectangular grid of points, 2009
- Seppo Mustonen, On lines and their intersection points in a rectangular grid of points, 2009 [Local copy]
- Seppo Mustonen, On lines going through a given number of points in a rectangular grid of points, 2010
- Seppo Mustonen, On lines going through a given number of points in a rectangular grid of points, 2010 [Local copy]
Showing 1-5 of 5 results.
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