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

1,2

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

Table of n, a(n) for n=1..61.

Eric Weisstein's World of Mathematics, Ellipse

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 *)

Crossrefs

Sequence in context: A054509 A134001 A338350 * A143218 A262024 A252117

Adjacent sequences: A088895 A088896 A088897 * A088899 A088900 A088901

Keyword

nonn,tabl

Author

Reinhard Zumkeller, Oct 21 2003

Status

approved