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A088897 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 A088897 #10 Feb 16 2025 08:32:51
%S A088897 5,7,13,9,19,29,11,25,35,49,13,31,45,63,81,15,37,55,73,91,113,17,43,
%T A088897 65,87,109,131,149,19,45,71,97,123,145,175,197,21,51,81,107,141,163,
%U A088897 197,223,253,23,57,91,121,159,185,219,245,279,317,25,63,101,135,169
%N A088897 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 A088897 T(n,k) = number of lattice points covered by an ellipse with semimajor axis = n, semiminor axis = k and center = (0,0).
%C A088897 a(n) = A088898(n) + A088899(n);
%C A088897 T(n,n) = A000328(n).
%H A088897 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Ellipse.html">Ellipse</a>
%t A088897 T[n_, k_] := Reduce[x^2/n^2 + y^2/k^2 <= 1, {x, y}, Integers] // Length;
%t A088897 Table[T[n, k], {n, 1, 11}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Sep 27 2021 *)
%Y A088897 Cf. A000328, A088898, A088899.
%K A088897 nonn,tabl
%O A088897 1,1
%A A088897 _Reinhard Zumkeller_, Oct 21 2003