

A194665


Number of k in [1,n] for which <n*r>+<k*r> > 1, where < > = fractional part and r = sqrt(2); row sums of A164664.


4



0, 2, 1, 3, 0, 2, 6, 2, 7, 1, 6, 12, 5, 12, 4, 11, 1, 8, 17, 6, 15, 2, 12, 23, 9, 21, 5, 17, 0, 12, 26, 8, 22, 2, 16, 32, 11, 28, 5, 22, 40, 16, 35, 10, 29, 2, 21, 42, 14, 36, 6, 28, 51, 20, 44, 11, 35, 1, 25, 51, 16, 42, 5, 32, 60, 22, 51, 11, 40, 70, 29, 60, 18, 49, 5, 36
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OFFSET

1,2


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000


MATHEMATICA

r = Sqrt[2]; z = 13;
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}]]
TableForm[Table[w[n, k], {n, 1, z}, {k, 1, n}]]
s[n_] := Sum[w[n, k], {k, 1, n}] (* A194663 *)
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}]]
(* A194664 *)
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}] (* A194665 *)


CROSSREFS

Cf. A194664.
Sequence in context: A025643 A127478 A127472 * A004563 A329647 A146094
Adjacent sequences: A194662 A194663 A194664 * A194666 A194667 A194668


KEYWORD

nonn


AUTHOR

Clark Kimberling, Sep 01 2011


STATUS

approved



