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A088898 T(n,k) = number of ordered pairs of integers (x,y) with x^2/n^2 + y^2/k^2 < 1, 1<=k<=n; triangular array, read by rows.

%I A088898 #8 Feb 16 2025 08:32:51
%S A088898 1,3,9,5,15,25,7,21,31,45,9,27,41,59,69,11,33,51,69,87,109,13,39,61,
%T A088898 83,105,127,145,15,41,67,93,119,141,171,193,17,47,77,103,137,159,193,
%U A088898 219,249,19,53,87,117,147,181,215,241,275,305,21,59,97,131,165,203
%N A088898 T(n,k) = number of ordered pairs of integers (x,y) with x^2/n^2 + y^2/k^2 < 1, 1<=k<=n; triangular array, read by rows.
%C A088898 T(n,k) = number of inner lattice points of an ellipse with semimajor axis = n, semiminor axis = k and center = (0,0).
%C A088898 a(n) = A088897(n) - A088899(n);
%C A088898 T(n,n) = A051132(n).
%H A088898 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Ellipse.html">Ellipse</a>
%t A088898 T[1, 1] = 1;
%t A088898 T[n_, k_] := Reduce[x^2/n^2 + y^2/k^2 < 1, {x, y}, Integers] // Length;
%t A088898 Table[T[n, k], {n, 1, 11}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Sep 27 2021 *)
%K A088898 nonn,tabl
%O A088898 1,2
%A A088898 _Reinhard Zumkeller_, Oct 21 2003