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%I #6 Mar 30 2012 18:57:43
%S 1,1,0,4,4,3,1,7,6,3,0,9,7,3,15,12,8,3,18,14,9,3,20,15,8,1,21,14,6,29,
%T 22,14,5,31,23,13,3,31,22,11,0,31,20,8,42,31,19,6,43,31,17,3,42,29,14,
%U 56,42,27,11,56,41,25,8,55,39,21,3,53,36,17,70,52,33,13,69,50
%N Number of k in [1,n] for which <n*r>+<k*r> > 1, where < > = fractional part and r = sqrt(3); row sums of A164667.
%t r = Sqrt[3]; z = 13;
%t p[x_] := FractionalPart[x]; f[x_] := Floor[x];
%t w[n_, k_] := p[r^n] + p[r^k] - p[r^n + r^k]
%t Flatten[Table[w[n, k], {n, 1, z}, {k, 1, n}]]
%t TableForm[Table[w[n, k], {n, 1, z}, {k, 1, n}]]
%t s[n_] := Sum[w[n, k], {k, 1, n}] (* A194666 *)
%t Table[s[n], {n, 1, 100}]
%t h[n_, k_] := f[p[n*r] + p[k*r]]
%t Flatten[Table[h[n, k], {n, 1, z}, {k, 1, n}]]
%t (* A194667 *)
%t TableForm[Table[h[n, k], {n, 1, z}, {k, 1, n}]]
%t t[n_] := Sum[h[n, k], {k, 1, n}]
%t Table[t[n], {n, 1, 100}] (* A194668 *)
%Y Cf. A194667.
%K nonn
%O 1,4
%A _Clark Kimberling_, Sep 01 2011
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