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A194210
a(n) = floor(Sum_{k=1..n} <k*Pi/3>), where < > denotes fractional part.
2
0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 6, 7, 8, 8, 9, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 13, 13, 14, 15, 15, 16, 17, 17, 18, 19, 20, 21, 21, 21, 21, 22, 22, 22, 22, 23, 23, 24, 24, 25, 25, 26, 27, 27, 28, 29, 30, 31, 32, 32, 32, 32, 32, 32, 32, 33, 33, 34, 34
OFFSET
1,9
MATHEMATICA
r = Pi/3;
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}] (* A194210 *)
s[n_] := Sum[a[k], {k, 1, n}]
Table[s[n], {n, 1, 100}] (* A194211 *)
CROSSREFS
Cf. A194211.
Sequence in context: A329547 A330560 A358466 * A112672 A025765 A029029
KEYWORD
nonn
AUTHOR
Clark Kimberling, Aug 19 2011
STATUS
approved