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A194677 Triangular array: T(n,k)=[<n*e>+<k*e>], where [ ] = floor, < > =  fractional part. 4
1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 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*e>+<k*e> > 1; see A194678.

LINKS

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

EXAMPLE

First eleven rows:

1

1 0

0 0 0

1 1 1 1

1 1 0 1 1

1 0 0 1 0 0

0 0 0 0 0 0 0

1 1 0 1 1 1 0 1

1 0 0 1 1 0 0 1 0

0 0 0 1 0 0 0 0 0 0

1 1 1 1 1 1 0 1 1 1 1

MATHEMATICA

r = E; 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}]]

(* A194675 *)

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

s[n_] := Sum[w[n, k], {k, 1, n}]  (* A194676 *)

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}]]

  (* A194677 *)

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}]  (* A194678 *)

CROSSREFS

Cf. A194678.

Sequence in context: A117964 A179020 A179771 * A194667 A094875 A012245

Adjacent sequences:  A194674 A194675 A194676 * A194678 A194679 A194680

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Sep 01 2011

STATUS

approved

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Last modified September 19 15:21 EDT 2019. Contains 327198 sequences. (Running on oeis4.)