login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A194163
a(n) = [sum{(k*r) : 1<=k<=n}], where [ ]=floor, ( )=fractional part, and r=sqrt(3).
3
0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 6, 7, 8, 9, 9, 10, 10, 11, 11, 12, 12, 12, 12, 13, 14, 14, 15, 16, 16, 16, 17, 18, 18, 18, 19, 19, 20, 20, 21, 21, 21, 22, 23, 23, 23, 24, 25, 25, 25, 26, 27, 27, 28, 29, 29, 29, 30, 31, 31, 31, 32, 33, 33, 33, 34, 34, 35, 36, 36
OFFSET
1,4
LINKS
MATHEMATICA
r = Sqrt[3];
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}] (* A194163 *)
s[n_] := Sum[a[k], {k, 1, n}]
Table[s[n], {n, 1, 100}] (* A194164 *)
PROG
(PARI) for(n=1, 50, print1(floor(sum(k=1, n, frac(k*sqrt(3)))), ", ")) \\ G. C. Greubel, Oct 29 2017
CROSSREFS
Cf. A194164.
Sequence in context: A075355 A287864 A347578 * A194253 A284849 A274618
KEYWORD
nonn
AUTHOR
Clark Kimberling, Aug 18 2011
STATUS
approved