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A194333 Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=n, r=2-tau, where tau=(1+sqrt(5))/2, the golden ratio. 2
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 0, 2, 1, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,24
COMMENTS
See A194285.
LINKS
EXAMPLE
First eleven rows:
1
1..1
1..1..1
1..1..1..1
1..1..1..1..1
1..1..1..1..1..1
0..1..2..1..1..1..1
1..1..1..1..1..1..1..1
1..1..1..2..1..0..2..0..1
1..1..1..1..1..1..1..1..1..1
1..1..1..1..2..1..0..1..1..1..1
MATHEMATICA
r = 2-GolenRatio;
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, n}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%] (* A194333 *)
CROSSREFS
Cf. A194333.
Sequence in context: A191898 A043290 A356153 * A203640 A043289 A063775
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 22 2011
STATUS
approved

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Last modified April 21 01:42 EDT 2024. Contains 371850 sequences. (Running on oeis4.)