A183137 [1/s]+[2/s]+...+[n/s], where s=(golden ratio)^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

1,4

Comments

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

Links

Table of n, a(n) for n=1..58.

Formula

floor(1/s)+floor(2/s)+...+floor(n/s), where s = (3+sqrt(5))/2 = (golden mean)^2.

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A225645 A302334 A024180 * A008738 A022790 A248360

Adjacent sequences: A183134 A183135 A183136 * A183138 A183139 A183140

Keyword

nonn

Author

Clark Kimberling, Dec 26 2010

Status

approved