A185541 a(n) = m*(m+1)/2, where m = floor(n^(3/2)).

1, 3, 15, 36, 66, 105, 171, 253, 378, 496, 666, 861, 1081, 1378, 1711, 2080, 2485, 2926, 3403, 4005, 4656, 5356, 6105, 6903, 7875, 8778, 9870, 11026, 12246, 13530, 14878, 16471, 17955, 19701, 21528, 23436, 25425, 27495, 29646, 31878, 34453, 37128, 39621, 42486, 45451, 48516, 52003, 55278, 58996, 62481, 66430, 70125, 74305, 78606, 83028, 87990, 92665, 97461, 102831

Offset

1,2

Comments

A subsequence of A000217, the triangular numbers.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Formula

a(n) = (1/2)*floor(n^3/2)*floor(1 + n^3/2).

Mathematica

f[n_]=Floor[n^(3/2)]*Floor[n^(3/2)+1]/2
Table[f[n], {n, 1, 80}]
(#(#+1))/2&/@Floor[Sqrt[Range[80]^3]] (* Harvey P. Dale, Feb 24 2023 *)

Prog

(Magma) [Floor(n^(3/2))*Floor(n^(3/2)+1)/2 : n in [1..60]]; // Vincenzo Librandi, Sep 13 2011

Crossrefs

Cf. A000217.

Sequence in context: A001803 A161738 A062741 * A372682 A176661 A117561

Adjacent sequences: A185538 A185539 A185540 * A185542 A185543 A185544

Keyword

nonn

Author

Clark Kimberling, Jan 30 2011

Status

approved