|
|
A194335
|
|
Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n^2, 1<=k<=n, r=2-tau, where tau=(1+sqrt(5))/2, the golden ratio.
|
|
2
|
|
|
1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6, 5, 4, 5, 6, 7, 5, 7, 6, 6, 7, 8, 7, 6, 8, 7, 8, 8, 8, 9, 7, 8, 8, 8, 8, 10, 8, 10, 9, 9, 9, 9, 9, 10, 10, 11, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 12, 11, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
|
|
LINKS
|
|
|
EXAMPLE
|
First eight rows:
1
2..2
3..3..3
4..4..4..4
5..5..6..5..4
5..6..7..5..7..6
6..7..8..7..6..8..7
8..8..8..9..7..8..8..8
|
|
MATHEMATICA
|
r = 2-GoldenRatio;
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^2}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|