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A194662 Number of k in [1,n] for which + > 1, where < > = fractional part and r = (1+sqrt(5))/2 (the golden ratio); row sums of A164661.

%I A194662 #5 Mar 30 2012 18:57:43
%S A194662 1,0,3,2,0,4,2,8,6,2,9,5,0,9,3,14,9,2,14,7,21,14,5,21,12,2,19,8,27,17,
%T A194662 5,25,13,0,22,8,32,18,3,28,13,40,25,8,37,20,2,32,13,45,27,7,40,20,55,
%U A194662 35,13,50,28,5,43,20,60,37,12,53,28,2,45,18,63,36,8,54,26,74,46
%N A194662 Number of k in [1,n] for which <n*r>+<k*r> > 1, where < > = fractional part and r = (1+sqrt(5))/2 (the golden ratio); row sums of A164661.
%t A194662 r = GoldenRatio; z = 14;
%t A194662 p[x_] := FractionalPart[x]; f[x_] := Floor[x];
%t A194662 h[n_, k_] := f[p[n*r] + p[k*r]]
%t A194662 Flatten[Table[h[n, k], {n, 1, z}, {k, 1, n}]]  (* A194661 *)
%t A194662 TableForm[Table[h[n, k], {n, 1, z}, {k, 1, n}]]
%t A194662 t[n_] := Sum[h[n, k], {k, 1, n}]
%t A194662 Table[t[n], {n, 1, 100}]   (* A194662 *)
%Y A194662 Cf. A194661.
%K A194662 nonn
%O A194662 1,3
%A A194662 _Clark Kimberling_, Sep 01 2011