A194251 [sum{(rk) : 1<=k<=n}], where [ ]=floor, ( )=fractional part, and r=3-sqrt(8).

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

Offset

1,5

Links

Table of n, a(n) for n=1..73.

Mathematica

r = 3-Sqrt[8];
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}]    (* A194251 *)
s[n_] := Sum[a[k], {k, 1, n}]
Table[s[n], {n, 1, 100}]   (* A194252 *)
Table[Floor[Sum[FractionalPart[k(3-Sqrt[8])], {k, n}]], {n, 80}] (* Harvey P. Dale, Dec 27 2024 *)

Crossrefs

Cf. A194252.

Sequence in context: A226591 A194223 A371587 * A029114 A224710 A210469

Adjacent sequences: A194248 A194249 A194250 * A194252 A194253 A194254

Keyword

nonn

Author

Clark Kimberling, Aug 20 2011

Status

approved