A373329 a(n)^2 is the greatest square not exceeding A000217(n^2).

0, 1, 3, 6, 11, 18, 25, 35, 45, 57, 71, 85, 102, 119, 138, 159, 181, 204, 229, 255, 283, 312, 342, 374, 407, 442, 478, 515, 554, 595, 636, 679, 724, 770, 817, 866, 916, 968, 1021, 1075, 1131, 1189, 1247, 1307, 1369, 1432, 1496, 1562, 1629, 1698, 1768, 1839, 1912

Offset: 0

Author

Hugo Pfoertner, Jun 01 2024

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000217, A000290, A001109 (subsequence), A001110, A001333, A037270, A061288.

Programs

Maple

a:= n-> floor(sqrt((t-> t*(t+1)/2)(n^2))):
seq(a(n), n=0..52);  # Alois P. Heinz, Jun 01 2024

Mathematica

Array[Floor@ Sqrt[(#^4 + #^2)/2] &, 53, 0] (* Michael De Vlieger, Jun 02 2024 *)

PARI

a(n) = sqrtint((n^4+n^2)/2)

Formula

a(n) = A061288(n^2). - Alois P. Heinz, Jun 01 2024