OFFSET
4,2
FORMULA
T(n,k) = round(sin((k+1)*Pi/n)/sin(Pi/n)), n >= 4, 1 <= k <= n-3.
EXAMPLE
Triangle begins:
1;
2, 2;
2, 2, 2;
2, 2, 2, 2;
2, 2, 3, 2, 2;
2, 3, 3, 3, 3, 2;
2, 3, 3, 3, 3, 3, 2;
2, 3, 3, 4, 4, 3, 3, 2;
2, 3, 3, 4, 4, 4, 3, 3, 2;
2, 3, 3, 4, 4, 4, 4, 3, 3, 2;
2, 3, 4, 4, 4, 4, 4, 4, 4, 3, 2;
2, 3, 4, 4, 5, 5, 5, 5, 4, 4, 3, 2;
2, 3, 4, 4, 5, 5, 5, 5, 5, 4, 4, 3, 2;
...
Row n lists the closest integers to the length of the diagonals drawn from a fixed vertex of a regular n-gon with unit edge length, n >= 4.
The lengths of the diagonals drawn from vertex A of a regular 8-gon ABCDEFGH with unit edge length are:
AC = 1.84775...
AD = 2.41421...
AE = 2.61312...
AF = 2.41421...
AG = 1.84775...
So the row for n=8 is 2, 2, 3, 2, 2.
MATHEMATICA
T[n_, k_]:=Round[Sin[(k+1)*Pi/n]/Sin[Pi/n]]; Flatten[Table[T[n, k], {n, 4, 16}, {k, 1, n-3}]] (* Stefano Spezia, Sep 07 2020 *)
CROSSREFS
KEYWORD
AUTHOR
Mohammed Yaseen, Aug 22 2020
STATUS
approved