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A194670 Triangular array: T(n,k)=[<n*r>+<k*r>], where [ ] = floor, < > =  fractional part, and r = sqrt(5). 3
0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1 (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 A194671.

LINKS

Table of n, a(n) for n=1..99.

EXAMPLE

First thirteen rows:

0

0 0

0 1 1

1 1 1 1

0 0 0 1 0

0 0 1 1 0 0

0 1 1 1 0 1 1

1 1 1 1 1 1 1 1

0 0 0 1 0 0 0 1 0

0 0 1 1 0 0 1 1 0 0

0 1 1 1 0 1 1 1 0 0 1

1 1 1 1 1 1 1 1 0 1 1 1

0 0 0 1 0 0 0 0 0 0 0 0 0

MATHEMATICA

r = Sqrt[5]; z = 13;

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}]]

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

s[n_] := Sum[w[n, k], {k, 1, n}]  (* A194669 *)

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}]]

(* A194670 *)

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}]  (* A194671 *)

CROSSREFS

Cf. A194671.

Sequence in context: A091247 A085137 A304577 * A130543 A193243 A281302

Adjacent sequences:  A194667 A194668 A194669 * A194671 A194672 A194673

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Sep 01 2011

STATUS

approved

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Last modified September 25 20:01 EDT 2020. Contains 337344 sequences. (Running on oeis4.)