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URL: https://oeis.org/A183137

⇱ A183137 - OEIS

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A183137
a(n) = [1/s] + [2/s] + ... + [n/s], where s = (golden ratio)^2 = (3+sqrt(5))/2 and [] = floor.
2
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+1) (the triangular numbers).
FORMULA
a(n+1) = a(n) + n - A005206(n). - John Furey, Jun 03 2015
EXAMPLE
a(7) = 7 = 0+0+1+1+1+2+2.
MATHEMATICA
Accumulate[With[{c=GoldenRatio^2}, Floor[Range[60]/c]]] (* Harvey P. Dale, Apr 20 2011 *)
KEYWORD
nonn
AUTHOR
Clark Kimberling, Dec 26 2010
STATUS
approved