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A194684
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Number of k in [1,n] for which <r^n>+<r^k> > 1, where < > = fractional part, and r=(1+sqrt(3))/2.
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4
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0, 2, 2, 2, 5, 3, 7, 1, 7, 8, 11, 3, 11, 12, 12, 0, 15, 6, 16, 19, 7, 5, 21, 12, 23, 0, 15, 15, 7, 15, 21, 10, 23, 8, 0, 24, 26, 19, 10, 0, 28, 29, 21, 39, 0, 43, 47, 24, 46, 39, 11, 3, 37, 40, 3, 49, 26, 51, 41, 3, 52, 23, 16, 57, 4, 3, 43, 45, 27, 13, 26, 68, 50, 49, 37
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OFFSET
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1,2
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LINKS
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MATHEMATICA
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r = 1/2 + Sqrt[3]/2; 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}]]
TableForm[Table[w[n, k], {n, 1, z}, {k, 1, n}]]
s[n_] := Sum[w[n, k], {k, 1, n}]
Table[s[n], {n, 1, 100}] (* A194684 *)
h[n_, k_] := f[p[n*r] + p[k*r]]
Flatten[Table[h[n, k], {n, 1, z}, {k, 1, n}]]
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}] (* A194686 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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