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 A194671 #5 Mar 30 2012 18:57:43 %S A194671 0,0,2,4,1,2,5,8,2,4,7,11,1,4,8,13,0,4,8,14,20,4,9,16,23,4,10,17,25,2, %T A194671 9,17,26,0,8,16,26,36,7,16,27,38,6,16,28,40,4,15,27,40,1,13,26,40,54, %U A194671 12,25,40,55,10,24,40,56,7,22,38,55,3,19,36,54,72,17,34,53,72 %N A194671 Number of k in [1,n] for which <n*r>+<k*r> > 1, where < > = fractional part and r = sqrt(5); row sums of A164670. %t A194671 r = Sqrt[5]; z = 13; %t A194671 p[x_] := FractionalPart[x]; f[x_] := Floor[x]; %t A194671 w[n_, k_] := p[r^n] + p[r^k] - p[r^n + r^k] %t A194671 Flatten[Table[w[n, k], {n, 1, z}, {k, 1, n}]] %t A194671 TableForm[Table[w[n, k], {n, 1, z}, {k, 1, n}]] %t A194671 s[n_] := Sum[w[n, k], {k, 1, n}] (* A194669 *) %t A194671 Table[s[n], {n, 1, 100}] %t A194671 h[n_, k_] := f[p[n*r] + p[k*r]] %t A194671 Flatten[Table[h[n, k], {n, 1, z}, {k, 1, n}]] %t A194671 (* A194670 *) %t A194671 TableForm[Table[h[n, k], {n, 1, z}, {k, 1, n}]] %t A194671 t[n_] := Sum[h[n, k], {k, 1, n}] %t A194671 Table[t[n], {n, 1, 100}] (* A194671 *) %Y A194671 Cf. A194670. %K A194671 nonn %O A194671 1,3 %A A194671 _Clark Kimberling_, Sep 01 2011