A337301 Triangle read by rows in which row n lists the closest integers to diagonal lengths of regular n-gon with unit edge length, n >= 4.
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
Offset: 4
Examples
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.
Crossrefs
Programs
-
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 *)
Formula
T(n,k) = round(sin((k+1)*Pi/n)/sin(Pi/n)), n >= 4, 1 <= k <= n-3.