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

0,4

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)).

Links

Table of n, a(n) for n=0..49.

Formula

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

Prog

(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

Crossrefs

Cf. A049472, A049473.

Sequence in context: A122781 A153355 A341274 * A310597 A310598 A024904

Adjacent sequences: A361792 A361793 A361794 * A361796 A361797 A361798

Keyword

nonn

Author

John Mason, Mar 24 2023

Status

approved