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A194665 Number of k in [1,n] for which + > 1, where < > = fractional part and r = sqrt(2); row sums of A164664.

%I A194665 #10 Feb 02 2018 16:20:17
%S A194665 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,
%T A194665 12,26,8,22,2,16,32,11,28,5,22,40,16,35,10,29,2,21,42,14,36,6,28,51,
%U A194665 20,44,11,35,1,25,51,16,42,5,32,60,22,51,11,40,70,29,60,18,49,5,36
%N 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.
%H A194665 G. C. Greubel, <a href="/A194665/b194665.txt">Table of n, a(n) for n = 1..10000</a>
%t A194665 r = Sqrt[2]; z = 13;
%t A194665 p[x_] := FractionalPart[x]; f[x_] := Floor[x];
%t A194665 w[n_, k_] := p[r^n] + p[r^k] - p[r^n + r^k]
%t A194665 Flatten[Table[w[n, k], {n, 1, z}, {k, 1, n}]]
%t A194665 TableForm[Table[w[n, k], {n, 1, z}, {k, 1, n}]]
%t A194665 s[n_] := Sum[w[n, k], {k, 1, n}]  (* A194663 *)
%t A194665 Table[s[n], {n, 1, 100}]
%t A194665 h[n_, k_] := f[p[n*r] + p[k*r]]
%t A194665 Flatten[Table[h[n, k], {n, 1, z}, {k, 1, n}]]
%t A194665    (* A194664 *)
%t A194665 TableForm[Table[h[n, k], {n, 1, z}, {k, 1, n}]]
%t A194665 t[n_] := Sum[h[n, k], {k, 1, n}]
%t A194665 Table[t[n], {n, 1, 100}]    (* A194665 *)
%Y A194665 Cf. A194664.
%K A194665 nonn
%O A194665 1,2
%A A194665 _Clark Kimberling_, Sep 01 2011