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

%I A386824 #10 Aug 07 2025 00:35:51
%S A386824 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,
%T A386824 85,1,65,17,73,5,89,25,113,1,41,85,5,97,53,13,65,145,1,101,13,109,29,
%U A386824 5,17,149,41,181,1,61,125,65,137,73,157,85,185,101,221
%N A386824 Triangle read by rows: T(n,k) = denominator((n^2 - k^2)/(n^2 + k^2)), where 0 <= k < n.
%H A386824 Stefano Spezia, <a href="/A386824/b386824.txt">First 150 rows of the triangle, flattened</a>
%F A386824 T(n,n-1) = A001844(n-1).
%e A386824 The triangle of the fractions begins as:
%e A386824   1/1;
%e A386824   1/1,   3/5;
%e A386824   1/1,   4/5,  5/13;
%e A386824   1/1, 15/17,   3/5,  7/25;
%e A386824   1/1, 12/13, 21/29,  8/17,  9/41;
%e A386824   1/1, 35/37,   4/5,   3/5,  5/13, 11/61;
%e A386824   1/1, 24/25, 45/53, 20/29, 33/65, 12/37, 13/85;
%e A386824   ...
%t A386824 T[n_,k_]:=Denominator[(n^2-k^2)/(n^2+k^2)]; Table[T[n,k],{n,11},{k,0,n-1}]//Flatten
%Y A386824 Cf. A000012 (k=0), A000290, A001844, A069011, A094728, A228564 (k=1), A243883 (k=2), A386823 (numerators).
%K A386824 nonn,easy,frac,look,tabl
%O A386824 1,3
%A A386824 _Stefano Spezia_, Aug 04 2025