A194171 [sum{(k*r) : 1<=k<=n}], where [ ]=floor, ( )=fractional part, and r=1/2+sqrt(5).

0, 1, 1, 2, 3, 3, 3, 4, 5, 5, 5, 6, 6, 7, 7, 8, 8, 8, 9, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 16, 16, 17, 18, 18, 19, 20, 20, 20, 21, 22, 22, 22, 23, 24, 24, 24, 25, 26, 26, 26, 27, 27, 27, 28, 29, 29, 30, 30, 31, 31, 32, 32, 33, 33, 33, 34, 35, 35, 36

Offset

1,4

Links

Table of n, a(n) for n=1..72.

Mathematica

r = 1/2 + Sqrt[5];
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}]   (* A194171 *)
s[n_] := Sum[a[k], {k, 1, n}]
Table[s[n], {n, 1, 100}]  (* A194172 *)

Crossrefs

Cf. A194172.

Sequence in context: A282692 A269371 A287355 * A004525 A049206 A194247

Adjacent sequences: A194168 A194169 A194170 * A194172 A194173 A194174

Keyword

nonn

Author

Clark Kimberling, Aug 18 2011

Status

approved