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A194296
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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<=n, 1<=k<=2^n, r=(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, 6, 7, 7, 6, 10, 11, 10, 12, 10, 11, 19, 19, 17, 19, 19, 17, 18, 32, 33, 32, 31, 33, 32, 31, 32, 57, 57, 57, 56, 57, 58, 56, 58, 56, 102, 102, 103, 102, 102, 103, 102, 103, 103, 102, 187, 186, 187, 185, 185, 186, 187, 187, 186, 187
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history;
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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 seven rows:
2
2...2
3...2...3
4...4...4...4
6...6...7...7...6
10..11..10..12..10..11
19..19..17..19..19..17..18
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MATHEMATICA
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r = 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[%] (* A194296 *)
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CROSSREFS
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Cf. A194285.
Sequence in context: A178994 A306608 A143976 * A194336 A127159 A025128
Adjacent sequences: A194293 A194294 A194295 * A194297 A194298 A194299
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling, Aug 21 2011
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STATUS
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approved
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