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A194686 Number of k in [1,n] for which <n*r>+<k*r> > 1, where < > = fractional part, and r=(1+sqrt(3))/2; row sums of A164685. 5
0, 2, 0, 1, 4, 1, 4, 8, 3, 7, 0, 4, 10, 1, 6, 13, 3, 10, 18, 6, 15, 1, 9, 19, 3, 13, 24, 7, 18, 30, 11, 24, 3, 15, 29, 6, 20, 35, 11, 26, 0, 15, 32, 4, 20, 38, 9, 27, 46, 15, 34, 1, 20, 41, 6, 26, 48, 12, 34, 57, 19, 43, 3, 26, 51, 9, 34, 60, 17, 43, 70, 25, 53, 6, 33, 62 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..76.

MATHEMATICA

r = 1/2 + Sqrt[3]/2; z = 15;

p[x_] := FractionalPart[x]; f[x_] := Floor[x];

w[n_, k_] := p[r^n] + p[r^k] - p[r^n + r^k]

Flatten[Table[w[n, k], {n, 1, z}, {k, 1, n}]]

  (* A194683 *)

TableForm[Table[w[n, k], {n, 1, z}, {k, 1, n}]]

s[n_] := Sum[w[n, k], {k, 1, n}]

Table[s[n], {n, 1, 100}]   (* A194684 *)

h[n_, k_] := f[p[n*r] + p[k*r]]

Flatten[Table[h[n, k], {n, 1, z}, {k, 1, n}]]

  (* A194685 *)

TableForm[Table[h[n, k], {n, 1, z}, {k, 1, n}]]

t[n_] := Sum[h[n, k], {k, 1, n}]

Table[t[n], {n, 1, 100}]    (* A194686 *)

CROSSREFS

Cf. A194684.

Sequence in context: A121583 A228924 A246862 * A266213 A124915 A158239

Adjacent sequences:  A194683 A194684 A194685 * A194687 A194688 A194689

KEYWORD

nonn

AUTHOR

Clark Kimberling, Sep 01 2011

STATUS

approved

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Last modified June 26 15:16 EDT 2017. Contains 288766 sequences.