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”).

A194330
Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=2n, 1<=k<=n, r=2-sqrt(3).
2
2, 2, 2, 2, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 1, 2, 2, 2, 2, 2, 2, 3, 1, 2, 3, 1, 3, 1, 3, 2, 2, 2, 2, 1, 3, 1, 2, 2, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 2, 2, 2, 1, 3, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 3, 2, 2, 2, 3
OFFSET
1,1
COMMENTS
See A194285.
EXAMPLE
First nine rows:
2
2..2
2..3..1
2..2..2..2
2..2..2..2..2
2..2..2..2..2..2
1..3..2..2..2..2..2
2..2..3..2..2..1..2..2
2..2..2..2..3..1..2..3..1
MATHEMATICA
r = 2-Sqrt[3];
f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
g[n_, k_] := Sum[f[n, k, i], {i, 1, 2n}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%] (* A194330 *)
CROSSREFS
Cf. A194285.
Sequence in context: A225538 A212355 A238646 * A280667 A194286 A063473
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 22 2011
STATUS
approved