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 A194669 #5 Mar 30 2012 18:57:43
%S A194669 0,0,0,0,3,0,2,0,3,0,4,0,5,0,7,0,0,0,2,0,3,0,8,0,8,0,13,0,3,0,2,0,14,
%T A194669 0,0,0,0,0,6,0,16,0,21,0,20,0,9,0,14,0,18,0,16,0,4,0,26,0,11,0,18,0,5,
%U A194669 0,30,0,20,0,32,0,21,0,21,0,20,0,13,0,20,0,13,0,30,0,19,0,10,0
%N A194669 Number of k in [1,n] for which <r^n>+<r^k> > 1, where < > = fractional part and r = sqrt(5).
%t A194669 r = Sqrt[5]; z = 13;
%t A194669 p[x_] := FractionalPart[x]; f[x_] := Floor[x];
%t A194669 w[n_, k_] := p[r^n] + p[r^k] - p[r^n + r^k]
%t A194669 Flatten[Table[w[n, k], {n, 1, z}, {k, 1, n}]]
%t A194669 TableForm[Table[w[n, k], {n, 1, z}, {k, 1, n}]]
%t A194669 s[n_] := Sum[w[n, k], {k, 1, n}] (* A194669 *)
%t A194669 Table[s[n], {n, 1, 100}]
%t A194669 h[n_, k_] := f[p[n*r] + p[k*r]]
%t A194669 Flatten[Table[h[n, k], {n, 1, z}, {k, 1, n}]]
%t A194669 (* A194670 *)
%t A194669 TableForm[Table[h[n, k], {n, 1, z}, {k, 1, n}]]
%t A194669 t[n_] := Sum[h[n, k], {k, 1, n}]
%t A194669 Table[t[n], {n, 1, 100}] (* A194671 *)
%K A194669 nonn
%O A194669 1,5
%A A194669 _Clark Kimberling_, Sep 01 2011