

A194678


Number of k in [1,n] for which <n*e>+<k*e> > 1, where < > = fractional part; row sums of A164677.


6



1, 1, 0, 4, 4, 2, 0, 6, 4, 1, 10, 8, 4, 0, 11, 7, 2, 16, 12, 7, 1, 17, 12, 5, 24, 18, 11, 3, 24, 17, 8, 32, 24, 15, 5, 31, 22, 11, 0, 29, 18, 6, 38, 27, 14, 1, 35, 22, 8, 45, 32, 17, 2, 41, 27, 11, 53, 38, 22, 5, 49, 33, 15, 62, 45, 27, 8, 57, 39, 19, 71, 52, 32, 11, 66, 46
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OFFSET

1,4


LINKS

Table of n, a(n) for n=1..76.


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. A194677.
Sequence in context: A141024 A173210 A058888 * A153015 A173635 A196766
Adjacent sequences: A194675 A194676 A194677 * A194679 A194680 A194681


KEYWORD

nonn


AUTHOR

Clark Kimberling, Sep 01 2011


STATUS

approved



