A194161 a(n) = [Sum_{k=1..n} (k*r)], where [ ]=floor, ( )=fractional part, and r=sqrt(2).

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

Offset

1,4

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Formula

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

Mathematica

r = Sqrt[2];
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}]   (* A194161 *)
s[n_] := Sum[a[k], {k, 1, n}]
Table[s[n], {n, 1, 100}]  (* A194162 *)

Prog

(PARI) a(n) = floor(sum(k=1, n, frac(k*sqrt(2)))); \\ Michel Marcus, Nov 06 2017

Crossrefs

Cf. A194162.

Sequence in context: A135636 A025795 A219610 * A051066 A029159 A029099

Adjacent sequences: A194158 A194159 A194160 * A194162 A194163 A194164

Keyword

nonn

Author

Clark Kimberling, Aug 18 2011

Status

approved