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A356119
Irregular table read by rows: T(n,k) is the number of k-sided polygons formed, for k>=3, in an equilateral triangle when straight line segments connect the three corner vertices to the points dividing the sides into n equal parts.
1
1, 6, 12, 3, 3, 1, 24, 6, 36, 9, 9, 7, 48, 24, 6, 72, 21, 15, 19, 84, 48, 12, 6, 108, 51, 33, 25, 132, 78, 18, 18, 168, 69, 51, 43, 180, 120, 48, 18, 216, 135, 57, 61, 252, 156, 66, 36, 294, 159, 105, 67, 312, 234, 84, 48, 372, 225, 117, 103, 408, 264, 138, 60, 456, 291, 159, 121, 486, 372, 138, 84
OFFSET
1,2
COMMENTS
The maximum sided k-gon up to n = 250 is the 6-gon; it is likely this is the maximum sided k-gon for all n.
See A092098 for more images of the triangle.
LINKS
FORMULA
Sum of row(n) = A092098(n).
EXAMPLE
The table begins:
1;
6;
12, 3, 3, 1;
24, 6;
36, 9, 9, 7;
48, 24, 6;
72, 21, 15, 19;
84, 48, 12, 6;
108, 51, 33, 25;
132, 78, 18, 18;
168, 69, 51, 43;
180, 120, 48, 18;
216, 135, 57, 61;
252, 156, 66, 36;
294, 159, 105, 67;
312, 234, 84, 48;
372, 225, 117, 103;
408, 264, 138, 60;
456, 291, 159, 121;
486, 372, 138, 84;
.
.
See the attached text file for more examples.
CROSSREFS
Cf. A092098 (regions), vertices (A331782), edges (A332376), A335413.
Sequence in context: A064913 A066401 A335413 * A263538 A076590 A113660
KEYWORD
nonn,tabf
AUTHOR
Scott R. Shannon, Jul 27 2022
STATUS
approved