A052146 a(n) = floor((sqrt(1+8*n)-3)/2).

0, 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11

Offset: 1

Author

N. J. A. Sloane, Jan 23 2000

Keywords

• nonn
• easy

References

• Richard P. Stanley, Enumerative Combinatorics, Vol. 2, Cambridge, 1999; see p. 450, Problem 7.2(d).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003056, A003881.

Programs

Mathematica

Floor[(Sqrt[1 + 8 Range[100]] - 3)/2] (* Wesley Ivan Hurt, Oct 02 2021 *)

PARI

a(n) = (sqrtint(1 + 8*n)-3)\2; \\ Amiram Eldar, Jun 27 2025

Formula

From Amiram Eldar, Jun 27 2025: (Start)

a(n) = A003056(n) - 1.

Sum_{n>=3} (-1)^(n+1)/a(n) = Pi/4 (A003881). (End)