This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A194668 #6 Mar 30 2012 18:57:43 %S A194668 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 A194668 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 A194668 56,42,27,11,56,41,25,8,55,39,21,3,53,36,17,70,52,33,13,69,50 %N A194668 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 A194668 r = Sqrt[3]; z = 13; %t A194668 p[x_] := FractionalPart[x]; f[x_] := Floor[x]; %t A194668 w[n_, k_] := p[r^n] + p[r^k] - p[r^n + r^k] %t A194668 Flatten[Table[w[n, k], {n, 1, z}, {k, 1, n}]] %t A194668 TableForm[Table[w[n, k], {n, 1, z}, {k, 1, n}]] %t A194668 s[n_] := Sum[w[n, k], {k, 1, n}] (* A194666 *) %t A194668 Table[s[n], {n, 1, 100}] %t A194668 h[n_, k_] := f[p[n*r] + p[k*r]] %t A194668 Flatten[Table[h[n, k], {n, 1, z}, {k, 1, n}]] %t A194668 (* A194667 *) %t A194668 TableForm[Table[h[n, k], {n, 1, z}, {k, 1, n}]] %t A194668 t[n_] := Sum[h[n, k], {k, 1, n}] %t A194668 Table[t[n], {n, 1, 100}] (* A194668 *) %Y A194668 Cf. A194667. %K A194668 nonn %O A194668 1,4 %A A194668 _Clark Kimberling_, Sep 01 2011