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

1,1

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

Table of n, a(n) for n=1..60.

Eric Weisstein's World of Mathematics, Ellipse

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 *)

Crossrefs

Cf. A000328, A088898, A088899.

Sequence in context: A335164 A205323 A105054 * A255233 A361708 A074755

Adjacent sequences: A088894 A088895 A088896 * A088898 A088899 A088900

Keyword

nonn,tabl

Author

Reinhard Zumkeller, Oct 21 2003

Status

approved