A361795 a(n) is the area of the largest rectangle with integer sides that can be drawn inside a circle of diameter n.

0, 0, 1, 4, 6, 12, 16, 20, 30, 36, 49, 56, 64, 81, 90, 110, 121, 144, 156, 169, 196, 210, 240, 256, 272, 306, 324, 361, 380, 420, 441, 462, 506, 529, 576, 600, 625, 676, 702, 756, 784, 812, 870, 900, 961, 992, 1056, 1089, 1122, 1190

Offset: 0

Author

John Mason, Mar 24 2023

Keywords

• nonn

Comments

Alternatively a(n) is the area of the largest rectangle with integer sides having a diagonal of length <= n.

a(n) = x*x or x*(x+1) for x=floor(n/sqrt(2)).

Crossrefs

Cf. A049472, A049473.

Programs

PARI

a(n)={my(t=sqrtint(n^2\2)); if(2*t*(t + 1) < n^2, t + 1, t)*t} \\ Andrew Howroyd, Mar 24 2023

PARI

a(n) = sqrtint(n^2\2) * ((sqrtint(2*n^2)+1)\2) \\ Andrew Howroyd, Mar 24 2023

Formula

a(n) = A049472(n) * A049473(n). - Andrew Howroyd, Mar 24 2023