A194167 [sum{(k*r) : 1<=k<=n}], where [ ]=floor, ( )=fractional part, and r=(3+sqrt(5))/2, the golden ratio.

0, 0, 0, 1, 1, 2, 3, 4, 4, 4, 4, 5, 5, 6, 7, 8, 8, 8, 8, 8, 9, 9, 10, 11, 12, 12, 12, 12, 13, 13, 14, 15, 16, 16, 16, 16, 16, 17, 18, 18, 19, 20, 20, 20, 21, 21, 22, 22, 23, 24, 24, 24, 24, 25, 25, 26, 27, 27, 28, 29, 29, 29, 29, 30, 31, 31, 32, 32, 33, 33, 33, 34, 34, 35

Offset

1,6

Links

Table of n, a(n) for n=1..74.

Mathematica

r = 1/2 + GoldenRatio;
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}]   (* A194167 *)
s[n_] := Sum[a[k], {k, 1, n}]
Table[s[n], {n, 1, 100}]  (* A194168 *)

Crossrefs

Cf. A194168.

Sequence in context: A087844 A287635 A189660 * A140427 A194816 A178770

Adjacent sequences: A194164 A194165 A194166 * A194168 A194169 A194170

Keyword

nonn

Author

Clark Kimberling, Aug 18 2011

Status

approved