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A194675 Triangular array: T(n,k)=[<e^n>+<e^k>], where [ ] = floor, < > =  fractional part. 5
1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 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 <e^n>+<e^k> > 1; see A194676.

LINKS

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

EXAMPLE

First ten rows:

1

1 0

0 0 0

1 0 0 1

1 0 0 1 0

1 0 0 1 0 0

1 1 0 1 1 1 1

1 1 1 1 1 1 1 1

0 0 0 0 0 0 0 1 0

1 0 0 1 0 0 1 1 0 0

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. A194676.

Sequence in context: A218171 A232714 A274179 * A117964 A179020 A179771

Adjacent sequences:  A194672 A194673 A194674 * A194676 A194677 A194678

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Sep 01 2011

STATUS

approved

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Last modified September 19 04:52 EDT 2019. Contains 327187 sequences. (Running on oeis4.)