A356790 Table read by antidiagonals: T(n,k) (n >= 1, k >= 1) is the number of regions formed by straight line segments when connecting the k-1 points along the top side of a rectangle to each of the k-1 points along the bottom side that divide these sides into k equal parts, along with straight lines that directly connect the n-1 points along the left side to the diametrically opposite point on the right side that divide these sides into n equal parts.
1, 2, 2, 6, 4, 3, 18, 10, 6, 4, 48, 24, 16, 8, 5, 106, 56, 34, 20, 10, 6, 216, 116, 70, 44, 26, 12, 7, 382, 228, 134, 84, 58, 30, 14, 8, 650, 396, 250, 152, 112, 60, 36, 16, 9, 1030, 666, 422, 272, 190, 112, 78, 40, 18, 10, 1564, 1048, 696, 448, 320, 196, 150, 84, 46, 20, 11
Offset: 1
Examples
The table begins: 1, 2, 6, 18, 48, 106, 216, 382, 650, 1030, 1564, 2258, 3210, 4386, 5926, ... 2, 4, 10, 24, 56, 116, 228, 396, 666, 1048, 1584, 2280, 3234, 4412, 5954, ... 3, 6, 16, 34, 70, 134, 250, 422, 696, 1082, 1622, 2322, 3280, 4462, 6008, ... 4, 8, 20, 44, 84, 152, 272, 448, 726, 1116, 1660, 2364, 3326, 4512, 6062, ... 5, 10, 26, 58, 112, 190, 320, 506, 794, 1194, 1748, 2462, 3434, 4630, 6190, ... 6, 12, 30, 60, 112, 196, 326, 512, 800, 1200, 1754, 2468, 3440, 4636, 6196, ... 7, 14, 36, 78, 150, 258, 418, 626, 936, 1358, 1934, 2670, 3664, 4882, 6464, ... 8, 16, 40, 84, 152, 256, 414, 632, 942, 1364, 1940, 2676, 3670, 4888, 6470, ... 9, 18, 46, 94, 172, 290, 468, 710, 1050, 1490, 2084, 2838, 3850, 5086, 6686, ... 10, 20, 50, 104, 188, 304, 480, 720, 1060, 1516, 2112, 2868, 3882, 5120, 6722, ... 11, 22, 56, 118, 218, 366, 586, 878, 1280, 1794, 2454, 3258, 4320, 5606, 7256, ... 12, 24, 60, 120, 208, 336, 518, 764, 1114, 1580, 2204, 2992, 4020, 5272, 6888, ... . . See the attached table for further terms.
Links
- Scott R. Shannon, Table for n=1..40, k=1..40.
- Scott R. Shannon, Image of T(3,4) = 34.
- Scott R. Shannon, Image of T(5,7) = 320.
- Scott R. Shannon, Image of T(8,6) = 256.
- Scott R. Shannon, Image of T(11,14) = 5606.
- Scott R. Shannon, Image of T(16,16) = 9964.
