A183137 a(n) = [1/s] + [2/s] + ... + [n/s], where s = (golden ratio)^2 = (3+sqrt(5))/2 and [] = floor.

0, 0, 1, 2, 3, 5, 7, 10, 13, 16, 20, 24, 28, 33, 38, 44, 50, 56, 63, 70, 78, 86, 94, 103, 112, 121, 131, 141, 152, 163, 174, 186, 198, 210, 223, 236, 250, 264, 278, 293, 308, 324, 340, 356, 373, 390, 407, 425, 443, 462, 481, 500, 520, 540, 561, 582, 603, 625

Offset: 1

Author

Clark Kimberling, Dec 26 2010

Keywords

• nonn

Comments

A183136(n) + a(n) = A000217(n+1) (the triangular numbers).

Examples

			a(7) = 7 = 0+0+1+1+1+2+2.
		

Links

• Johan Kok, Integer sequences with conjectured relation with certain graph parameters of the family of linear Jaco graphs, arXiv:2507.16500 [math.CO], 2025. See p. 4.

Crossrefs

Cf. A001622, A104457, A183136, A000217, A005206, A060143, A060144.

Programs

Mathematica

Accumulate[With[{c=GoldenRatio^2},Floor[Range[60]/c]]]  (* Harvey P. Dale, Apr 20 2011 *)

Formula

a(n+1) = a(n) + n - A005206(n). - John Furey, Jun 03 2015