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A194681 Triangular array: T(n,k)=[<n*r>+<k*r>], where [ ] = floor, < > =  fractional part, and r=3-sqrt(2). 4
1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

n-th row sum gives number of k in [0,1] for which <n*r>+<k*r> > 1; see A194678.

LINKS

G. C. Greubel, Table of n, a(n) for the first 150 rows, flattened

EXAMPLE

First ten rows:

1

0 0

1 0 1

0 0 1 0

1 1 1 1 1

1 0 1 0 1 1

0 0 0 0 1 0 0

1 0 1 1 1 1 0 1

0 0 1 0 1 0 0 0 0

1 1 1 1 1 1 0 1 1 1

MATHEMATICA

r = 3 - Sqrt[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}]]

  (* A194679 *)

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

s[n_] := Sum[w[n, k], {k, 1, n}]  (* A194680 *)

Table[s[n], {n, 1, 100}]

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

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

  (* A194681 *)

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}]   (* A194682 *)

PROG

(PARI) for(n=1, 10, for(k=1, n, print1(floor(frac(n*(3-sqrt(2))) + frac(k*(3-sqrt(2)))), ", "))) \\ G. C. Greubel, Feb 08 2018

CROSSREFS

Cf. A194682.

Sequence in context: A232990 A285076 A267598 * A065043 A189298 A288375

Adjacent sequences:  A194678 A194679 A194680 * A194682 A194683 A194684

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Sep 01 2011

STATUS

approved

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Last modified September 19 10:57 EDT 2019. Contains 327192 sequences. (Running on oeis4.)