A194208 a(n) = [Sum_{k=1..n} (k*Pi/2)], where [ ]=floor, ( )=fractional part.

0, 0, 1, 1, 2, 2, 3, 4, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 10, 11, 12, 12, 13, 13, 14, 14, 15, 16, 16, 17, 17, 18, 18, 19, 20, 20, 20, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 27, 27, 27, 28, 28, 29, 30, 30, 31, 31, 32, 32, 33, 33, 34, 35, 35, 36, 36, 37, 37, 38, 38, 39

Offset

1,5

Links

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

Mathematica

r = Pi/2;
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}]  (* A194208 *)
s[n_] := Sum[a[k], {k, 1, n}]
Table[s[n], {n, 1, 100}] (* A194209 *)

Prog

(PARI) a(n) = floor(sum(k=1, n, frac(k*Pi/2))); \\ Michel Marcus, Apr 10 2021

Crossrefs

Cf. A194209.

Sequence in context: A047783 A321667 A194212 * A057358 A038128 A097337

Adjacent sequences: A194205 A194206 A194207 * A194209 A194210 A194211

Keyword

nonn

Author

Clark Kimberling, Aug 19 2011

Status

approved