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A194682 Number of k in [1,n] for which + > 1, where < > = fractional part, and r=3-sqrt(2); row sums of A164681.

%I A194682 #11 Feb 25 2018 13:17:45
%S A194682 1,0,2,1,5,4,1,6,2,9,5,0,8,2,11,5,16,10,2,14,6,20,11,1,16,5,22,11,29,
%T A194682 18,5,24,11,32,19,4,26,10,34,18,1,26,8,34,16,44,26,6,35,14,45,24,2,34,
%U A194682 11,45,22,57,34,9,45,20,58,32,5,44,16,57,29,0,42,12,55,25,70,40
%N A194682 Number of k in [1,n] for which <n*r>+<k*r> > 1, where < > = fractional part, and r=3-sqrt(2); row sums of A164681.
%H A194682 G. C. Greubel, <a href="/A194682/b194682.txt">Table of n, a(n) for n = 1..5000</a>
%t A194682 r = 3 - Sqrt[2]; z = 15;
%t A194682 p[x_] := FractionalPart[x]; f[x_] := Floor[x];
%t A194682 w[n_, k_] := p[r^n] + p[r^k] - p[r^n + r^k]
%t A194682 Flatten[Table[w[n, k], {n, 1, z}, {k, 1, n}]]
%t A194682   (* A194679 *)
%t A194682 TableForm[Table[w[n, k], {n, 1, z}, {k, 1, n}]]
%t A194682 s[n_] := Sum[w[n, k], {k, 1, n}]  (* A194680 *)
%t A194682 Table[s[n], {n, 1, 100}]
%t A194682 h[n_, k_] := f[p[n*r] + p[k*r]]
%t A194682 Flatten[Table[h[n, k], {n, 1, z}, {k, 1, n}]]
%t A194682   (* A194681 *)
%t A194682 TableForm[Table[h[n, k], {n, 1, z}, {k, 1, n}]]
%t A194682 t[n_] := Sum[h[n, k], {k, 1, n}]
%t A194682 Table[t[n], {n, 1, 100}]   (* A194682 *)
%o A194682 (PARI) for(n=1, 50, print1(sum(k=1,n, floor(frac(n*(3-sqrt(2))) + frac(k*(3-sqrt(2))))), ", ")) \\ _G. C. Greubel_, Feb 08 2018
%Y A194682 Cf. A194681.
%K A194682 nonn
%O A194682 1,3
%A A194682 _Clark Kimberling_, Sep 01 2011