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

1,2

Links

Table of n, a(n) for n=1..66.

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.

Formula

T(1,k) = A306302(k-2) + 2, k >= 2.

T(2,k) = 2*A355902(k-2) + 4 = A306302(k-2) + 2*k, k >= 2.

T(n,1) = n.

T(n,2) = 2n.

T(n,3) = A146951(n).

Example

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, ...
.
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See the attached table for further terms.

Crossrefs

Cf. A146951, A355798, A306302, A290131, A331452, A355902.

Sequence in context: A305353 A134458 A193819 * A182786 A343187 A009279

Adjacent sequences: A356787 A356788 A356789 * A356791 A356792 A356793

Keyword

nonn,tabl

Author

Scott R. Shannon and N. J. A. Sloane, Sep 04 2022

Status

approved