A386824 Triangle read by rows: T(n,k) = denominator((n^2 - k^2)/(n^2 + k^2)), where 0 <= k < n.

1, 1, 5, 1, 5, 13, 1, 17, 5, 25, 1, 13, 29, 17, 41, 1, 37, 5, 5, 13, 61, 1, 25, 53, 29, 65, 37, 85, 1, 65, 17, 73, 5, 89, 25, 113, 1, 41, 85, 5, 97, 53, 13, 65, 145, 1, 101, 13, 109, 29, 5, 17, 149, 41, 181, 1, 61, 125, 65, 137, 73, 157, 85, 185, 101, 221

Offset: 1

Author

Stefano Spezia, Aug 04 2025

Keywords

• nonn
• easy
• frac
• look
• tabl

Examples

			The triangle of the fractions begins as:
  1/1;
  1/1,   3/5;
  1/1,   4/5,  5/13;
  1/1, 15/17,   3/5,  7/25;
  1/1, 12/13, 21/29,  8/17,  9/41;
  1/1, 35/37,   4/5,   3/5,  5/13, 11/61;
  1/1, 24/25, 45/53, 20/29, 33/65, 12/37, 13/85;
  ...
		

Links

• Stefano Spezia, First 150 rows of the triangle, flattened

Crossrefs

Cf. A000012 (k=0), A000290, A001844, A069011, A094728, A228564 (k=1), A243883 (k=2), A386823 (numerators).

Programs

Mathematica

T[n_,k_]:=Denominator[(n^2-k^2)/(n^2+k^2)]; Table[T[n,k],{n,11},{k,0,n-1}]//Flatten

Formula

T(n,n-1) = A001844(n-1).