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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)
A194679-A194682: r=3-sqrt(2)
A194683-A194686: r=(1+sqrt(3))/2
LINKS
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: A072770 A090172 A284369 * A285427 A285621 A204435
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Sep 01 2011
STATUS
approved

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Last modified March 28 16:58 EDT 2024. Contains 371254 sequences. (Running on oeis4.)