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.

5, 7, 13, 9, 19, 29, 11, 25, 35, 49, 13, 31, 45, 63, 81, 15, 37, 55, 73, 91, 113, 17, 43, 65, 87, 109, 131, 149, 19, 45, 71, 97, 123, 145, 175, 197, 21, 51, 81, 107, 141, 163, 197, 223, 253, 23, 57, 91, 121, 159, 185, 219, 245, 279, 317, 25, 63, 101, 135, 169

Offset: 1

Author

Reinhard Zumkeller, Oct 21 2003

Keywords

• nonn
• tabl

Comments

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

a(n) = A088898(n) + A088899(n);

T(n,n) = A000328(n).

Links

• Eric Weisstein's World of Mathematics, Ellipse

Crossrefs

Cf. A000328, A088898, A088899.

Programs

Mathematica

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 *)