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.

1, 3, 9, 5, 15, 25, 7, 21, 31, 45, 9, 27, 41, 59, 69, 11, 33, 51, 69, 87, 109, 13, 39, 61, 83, 105, 127, 145, 15, 41, 67, 93, 119, 141, 171, 193, 17, 47, 77, 103, 137, 159, 193, 219, 249, 19, 53, 87, 117, 147, 181, 215, 241, 275, 305, 21, 59, 97, 131, 165, 203

Offset: 1

Author

Reinhard Zumkeller, Oct 21 2003

Keywords

• nonn
• tabl

Comments

T(n,k) = number of inner lattice points of an ellipse with semimajor axis = n, semiminor axis = k and center = (0,0).

a(n) = A088897(n) - A088899(n);

T(n,n) = A051132(n).

Links

• Eric Weisstein's World of Mathematics, Ellipse

Programs

Mathematica

T[1, 1] = 1;
T[n_, k_] := Reduce[x^2/n^2 + y^2/k^2 < 1, {x, y}, Integers] // Length;
Table[T[n, k], {n, 1, 11}, {k, 1, n}] // Flatten (* Jean-François Alcover, Sep 27 2021 *)