A356790 - OEIS

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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.

3

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

(list; table; graph; refs; listen; history; text; internal format)

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, ...

.

.

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