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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.
2
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
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
KEYWORD
nonn,tabl
AUTHOR
Reinhard Zumkeller, Oct 21 2003
STATUS
approved