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A194310
Triangular array: g(n,k)=number of fractional parts (i*e) in interval [(k-1)/n, k/n], for 1<=i<=2n, 1<=k<=n.
2
2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 3, 1, 3, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 1, 2, 3, 1, 2, 2, 2, 3, 1, 2, 2, 2, 1, 3, 3, 1, 2, 3, 1, 2, 3, 1, 2, 2, 2, 2, 2, 2, 3, 2, 1, 2, 2, 3, 1, 2, 3, 1, 3, 2, 2, 2, 1, 2, 1, 3, 1, 3, 1, 3, 1, 3, 2, 2, 2, 2, 2, 2, 3, 1, 2, 2, 3, 1
OFFSET
1,1
COMMENTS
See A194285.
EXAMPLE
First nine rows:
2
2..2
2..2..2
2..2..3..1
3..1..3..2..1
2..2..2..2..2..2
2..2..2..2..2..2..2
2..2..2..3..2..2..2..1
2..3..1..2..2..2..3..1..2
MATHEMATICA
r = E;
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[%] (* A194310 *)
CROSSREFS
Cf. A194285.
Sequence in context: A257773 A164898 A100801 * A306227 A359455 A363853
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 21 2011
STATUS
approved