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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.
1
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
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
KEYWORD
nonn,tabl
AUTHOR
Scott R. Shannon, Aug 18 2022
STATUS
approved