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A194661 Triangular array: T(n,k)=[<n*r>+<k*r>], where [ ] = floor, < > =  fractional part, and r = (1+sqrt(5))/2 (the golden ratio). 2
1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

n-th row sum gives the number of k in [0,n] for which <n*r>+<k*r> > 1; see A194662.

Triangles of this sort and their row sums are sampled by the following sequences:

A194661-A194662: r=(1+sqrt(5))/2

A194663-A194665: r=sqrt(2)

A194666-A194668: r=sqrt(3)

A194669-A194671: r=sqrt(5)

A194675-A194678: r=e

A194679-A194682: r=3-sqrt(2)

A194683-A194686: r=(1+sqrt(3))/2

LINKS

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

EXAMPLE

First 13 rows:

1

0 0

1 1 1

1 0 1 0

0 0 0 0 0

1 0 1 1 0 1

0 0 1 0 0 1 0

1 1 1 1 1 1 1 1

1 0 1 1 0 1 0 1 1

0 0 1 0 0 0 0 1 0 0

1 1 1 1 0 1 1 1 1 0 1

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

0 0 0 0 0 0 0 0 0 0 0 0 0

MATHEMATICA

r = GoldenRatio; z = 14;

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

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

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

(* A194661 *)

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}]   (* A194662 *)

CROSSREFS

Cf. A194662.

Sequence in context: A071674 A090172 A284369 * A285427 A285621 A204435

Adjacent sequences:  A194658 A194659 A194660 * A194662 A194663 A194664

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Sep 01 2011

STATUS

approved

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Last modified July 28 17:07 EDT 2021. Contains 346335 sequences. (Running on oeis4.)