A108914
Number of regions formed inside square by diagonals and the segments joining the vertices to the points dividing the sides into n equal length segments.
Original entry on oeis.org
4, 32, 96, 188, 332, 460, 712, 916, 1204, 1488, 1904, 2108, 2716, 3080, 3532, 4068, 4772, 5140, 6016, 6392, 7188, 7992, 8936, 9260, 10484, 11312, 12208, 12968, 14396, 14660, 16504, 17220, 18436, 19680, 20756, 21548, 23692, 24728, 25992, 26868, 29204, 29704, 32176, 33068, 34444, 36552, 38552
Offset: 1
Len Smiley and Brian Wick ( mathclub(AT)math.uaa.alaska.edu ), Jul 19 2005
- Scott R. Shannon, Table of n, a(n) for n = 1..100
- 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 = 11.
- Scott R. Shannon, Image for n = 30.
- L. Smiley, The case n=6. Note 3- and 4-fold off-diagonal concurrencies.
- L. Smiley, The case n=7. Note there are no off-diagonal concurrencies.
A092098 is the corresponding count for triangles.
A355949
Number of vertices formed in a square by straight line segments when connecting the four corner vertices to the points dividing the sides into n equal parts.
Original entry on oeis.org
5, 25, 81, 157, 301, 381, 665, 821, 1109, 1353, 1825, 1861, 2621, 2881, 3285, 3813, 4645, 4773, 5873, 5953, 6821, 7665, 8761, 8613, 10165, 10921, 11777, 12337, 14173, 13717, 16265, 16581, 17861, 19161, 20093, 20461, 23405, 24145, 25305, 25701, 28885, 28433, 31841, 32077, 33269, 35841, 38185
Offset: 1
A355992
Irregular table read by rows: T(n,k) is the number of k-sided polygons formed, for k>=3, in a square when straight line segments connect the four corner vertices to the points dividing the sides into n equal parts.
Original entry on oeis.org
4, 24, 8, 56, 28, 12, 96, 80, 8, 4, 144, 140, 36, 12, 216, 216, 24, 4, 272, 332, 76, 24, 8, 360, 448, 80, 28, 456, 572, 132, 36, 8, 568, 728, 128, 64, 656, 916, 260, 28, 40, 4, 792, 1104, 176, 36, 928, 1308, 316, 128, 32, 4, 1064, 1568, 304, 128, 16, 1240, 1772, 396, 88, 32, 4, 1416, 2032, 432, 156, 32
Offset: 1
The table begins:
4;
24, 8;
56, 28, 12;
96, 80, 8, 4;
144, 140, 36, 12;
216, 216, 24, 4;
272, 332, 76, 24, 8;
360, 448, 80, 28;
456, 572, 132, 36, 8;
568, 728, 128, 64;
656, 916, 260, 28, 40, 4;
792, 1104, 176, 36;
928, 1308, 316, 128, 32, 4;
1064, 1568, 304, 128, 16;
1240, 1772, 396, 88, 32, 4;
1416, 2032, 432, 156, 32;
.
.
A357061
Number of edges in a square when n internal squares are drawn between the 4n points that divide each side into n+1 equal parts.
Original entry on oeis.org
4, 12, 36, 76, 132, 180, 292, 348, 516, 604, 804, 892, 1156, 1284, 1572, 1708, 2052, 2180, 2596, 2796, 3204, 3412, 3876, 4012, 4612, 4860, 5412, 5668, 6276, 6508, 7204, 7460, 8172, 8524, 9252, 9516, 10372, 10740, 11532, 11900, 12804, 13100, 14116, 14532, 15468, 15940, 16932, 17196, 18436
Offset: 0
Showing 1-4 of 4 results.
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