A065737 Largest square <= binomial(n,2).

0, 1, 1, 4, 9, 9, 16, 25, 36, 36, 49, 64, 64, 81, 100, 100, 121, 144, 169, 169, 196, 225, 225, 256, 289, 324, 324, 361, 400, 400, 441, 484, 484, 529, 576, 625, 625, 676, 729, 729, 784, 841, 900, 900, 961, 1024, 1024, 1089, 1156, 1225, 1225, 1296, 1369, 1369, 1444

Offset: 1

Author

Labos Elemer, Nov 15 2001

Keywords

• easy
• nonn

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A048760, A000217, A000290, A061288, A065730-A065741.

Programs

Mathematica

Floor[Sqrt[#]]^2&/@Binomial[Range[50],2] (* Harvey P. Dale, Feb 28 2020 *)

PARI

a(n) = { sqrtint(binomial(n, 2))^2 } \\ Harry J. Smith, Oct 28 2009

Formula

a(n) = A048760(binomial(n,2)).

a(n) = A061288(n-1)^2 = A000290(A061288(n-1)) for n>=2. - Alois P. Heinz, Nov 07 2024