A354544 Table read by antidiagonals: T(n,k) (n >= 3, k >= 1) is the number of vertices formed in a regular n-gon by straight line segments when connecting the n corner vertices to the points dividing the sides into k equal parts.

3, 7, 5, 21, 25, 10, 25, 81, 61, 19, 63, 157, 285, 205, 42, 67, 301, 476, 541, 358, 57, 129, 381, 1020, 1327, 1526, 681, 135, 133, 665, 1311, 2185, 2682, 2417, 1234, 171, 219, 821, 2215, 3067, 5250, 5073, 4716, 2131, 341, 223, 1109, 2666, 4921, 7246, 8937, 8623, 6861, 3169, 313

Offset

3,1

Links

Table of n, a(n) for n=3..57.

Scott R. Shannon, Image of T(4,9) = 1109.

Scott R. Shannon, Image of T(5,7) = 2215.

Scott R. Shannon, Image of T(7,6) = 7246.

Scott R. Shannon, Image of T(10,3) = 6861.

Scott R. Shannon, Image of T(11,4) = 21143.

Scott R. Shannon, Table for n=3..25.

Formula

T(n,1) = A007569(n).

T(3,k) = A331782(k).

T(4,k) = A355949(k).

Example

The table begins:
3,    7,     21,     25,     63,     67,     129,    133,     219,     223,...
5,    25,    81,     157,    301,    381,    665,    821,     1109,    1353,...
10,   61,    285,    476,    1020,   1311,   2215,   2666,    3810,    4421,...
19,   205,   541,    1327,   2185,   3067,   4921,   6739,    8401,    10507,...
42,   358,   1526,   2682,   5250,   7246,   11214,  14050,   19418,   23094,...
57,   681,   2417,   5073,   8937,   13089,  19473,  26049,   33769,   42497,...
135,  1234,  4716,   8623,   16173,  22780,  34398,  43813,   59391,   71614,...
171,  2131,  6861,   14271,  24731,  36161,  53071,  70751,   91761,   115001,...
341,  3169,  11451,  21143,  38665,  55221,  81983,  105403,  141405,  171689,...
313,  4837,  14653,  31009,  53989,  78589,  115909, 154105,  199777,  249961,...
728,  6787,  23491,  43850,  78858,  113517, 166829, 215788,  287404,  350663,...
771,  9927,  30479,  61951,  105155, 157851, 224043, 299727,  386807,  485367,...
1380, 12856, 43080,  81136,  144180, 208636, 304500, 395536,  524040,  641656,...
1393, 17633, 54001,  109265, 184785, 277745, 392737, 525169,  677729,  849249,...
2397, 22288, 73066,  138177, 243355, 353686, 513264, 668815,  882793,  1083564,...
1855, 27595, 88291,  177085, 302167, 450469, 641539, 855829,  1106119, 1384183,...
3895, 36139, 116337, 220933, 386403, 563351, 814093, 1063393, 1399407, 1721059,...
.
.
See the attached text file for more examples and the cross references for further images.

Crossrefs

Cf. A356044 (number of regions), A007569 (first column), A331782 (first row), A355949 (second row).

Sequence in context: A282598 A269369 A305421 * A112071 A231609 A046561

Adjacent sequences: A354541 A354542 A354543 * A354545 A354546 A354547

Keyword

nonn,tabl

Author

Scott R. Shannon, Aug 18 2022

Status

approved