A194253 [sum{(rk) : 1<=k<=n}], where [ ]=floor, ( )=fractional part, and r=sqrt(12).

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

Offset

1,4

Links

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

Mathematica

r = Sqrt[12];
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}]    (* A194253 *)
s[n_] := Sum[a[k], {k, 1, n}]
Table[s[n], {n, 1, 100}]   (* A194254 *)

Crossrefs

Cf. A194253.

Sequence in context: A287864 A347578 A194163 * A284849 A274618 A176843

Adjacent sequences: A194250 A194251 A194252 * A194254 A194255 A194256

Keyword

nonn

Author

Clark Kimberling, Aug 20 2011

Status

approved