A194324 - OEIS

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A194324 - OEIS

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A194324

Triangular array: g(n,k)=number of fractional parts (i*sqrt(1/2)) in interval [(k-1)/n, k/n], for 1<=i<=2^n, 1<=k<=n.

2

2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 6, 6, 6, 8, 6, 11, 10, 11, 11, 11, 10, 19, 18, 18, 19, 18, 19, 17, 33, 32, 31, 32, 32, 32, 32, 32, 56, 58, 57, 57, 57, 56, 57, 56, 58, 103, 102, 102, 103, 102, 102, 103, 103, 102, 102, 186, 186, 188, 184, 188, 186, 185, 187, 186, 186

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

LINKS

Table of n, a(n) for n=1..65.

EXAMPLE

First eight rows:

2

2...2

2...3...3

4...4...4...4

6...6...6...8...6

11..10..11..11..11..10

19..18..18..19..18..19..17

33..32..31..32..32..32..32..32

MATHEMATICA

r = Sqrt[1/2];

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[%] (* A194324 *)

CROSSREFS

Sequence in context: A109497 A156078 A123919 * A194328 A194304 A090701

Adjacent sequences: A194321 A194322 A194323 * A194325 A194326 A194327

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 22 2011

STATUS

approved