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A194336
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Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=2^n, 1<=k<=n, r=2-tau, where tau=(1+sqrt(5))/2, the golden ratio.
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2
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2, 2, 2, 3, 2, 3, 4, 4, 4, 4, 6, 7, 7, 6, 6, 11, 10, 12, 10, 11, 10, 18, 17, 19, 19, 17, 19, 19, 32, 31, 32, 33, 31, 32, 33, 32, 56, 58, 56, 58, 57, 56, 57, 57, 57, 102, 103, 103, 102, 103, 102, 102, 103, 102, 102, 185, 187, 186, 187, 187, 186, 185, 185, 187, 186
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OFFSET
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1,1
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COMMENTS
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See A194285.
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LINKS
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Table of n, a(n) for n=1..65.
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EXAMPLE
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First eight rows:
2
2...2
3...2...3
4...4...4...4
6...7...7...6...6
11..10..12..10..11..10
18..17..19..19..17..19..19
32..31..32..33..31..32..33..32
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MATHEMATICA
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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, 2^n}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%] (* A194336 *)
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CROSSREFS
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Cf. A194285.
Sequence in context: A306608 A143976 A194296 * A127159 A025128 A058769
Adjacent sequences: A194333 A194334 A194335 * A194337 A194338 A194339
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling, Aug 22 2011
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STATUS
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approved
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