

A194288


Triangular array: g(n,k)=number of fractional parts (i*sqrt(2)) in interval [(k1)/n, k/n], for 1<=i<=2^n, 1<=k<=n.


2



2, 2, 2, 3, 3, 2, 4, 4, 4, 4, 6, 7, 7, 6, 6, 11, 11, 11, 10, 11, 10, 19, 18, 19, 18, 18, 18, 18, 32, 33, 31, 33, 31, 32, 32, 32, 57, 56, 58, 57, 57, 57, 56, 57, 57, 103, 102, 103, 102, 104, 101, 103, 102, 103, 101, 187, 184, 187, 186, 187, 187, 185, 186, 186, 188
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OFFSET

1,1


COMMENTS

See A194285.


LINKS

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


EXAMPLE

First eight rows:
2
2...2
3...3...2
4...4...4...4
6...7...7...6...6
11..11..11..10..11..10
19..18..19..18..18..18..18
32..33..31..33..31..32..32..32


MATHEMATICA

r = Sqrt[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[%] (* A194288 *)


CROSSREFS

Cf. A194285.
Sequence in context: A116505 A110534 A194340 * A194332 A322062 A071451
Adjacent sequences: A194285 A194286 A194287 * A194289 A194290 A194291


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Aug 21 2011


STATUS

approved



