A194239 a(n) = [Sum_{k=1..n} (r*k)], where [ ]=floor, ( )=fractional part, and r=(1+sqrt(2))/2.

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

Offset

1,4

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Mathematica

r = (1+Sqrt[2])/2;
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}]    (* A194239 *)
s[n_] := Sum[a[k], {k, 1, n}]
Table[s[n], {n, 1, 100}]   (* A194240 *)

Crossrefs

Cf. A194240.

Sequence in context: A119026 A064775 A260731 * A064475 A025774 A280168

Adjacent sequences: A194236 A194237 A194238 * A194240 A194241 A194242

Keyword

nonn

Author

Clark Kimberling, Aug 20 2011

Status

approved