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A194678 Number of k in [1,n] for which + > 1, where < > = fractional part; row sums of A164677.

%I A194678 #5 Mar 30 2012 18:57:43
%S A194678 1,1,0,4,4,2,0,6,4,1,10,8,4,0,11,7,2,16,12,7,1,17,12,5,24,18,11,3,24,
%T A194678 17,8,32,24,15,5,31,22,11,0,29,18,6,38,27,14,1,35,22,8,45,32,17,2,41,
%U A194678 27,11,53,38,22,5,49,33,15,62,45,27,8,57,39,19,71,52,32,11,66,46
%N A194678 Number of k in [1,n] for which <n*e>+<k*e> > 1, where < > = fractional part; row sums of A164677.
%t A194678 r = E; z = 15;
%t A194678 p[x_] := FractionalPart[x]; f[x_] := Floor[x];
%t A194678 w[n_, k_] := p[r^n] + p[r^k] - p[r^n + r^k]
%t A194678 Flatten[Table[w[n, k], {n, 1, z}, {k, 1, n}]]
%t A194678 (* A194675 *)
%t A194678 TableForm[Table[w[n, k], {n, 1, z}, {k, 1, n}]]
%t A194678 s[n_] := Sum[w[n, k], {k, 1, n}]  (* A194676 *)
%t A194678 Table[s[n], {n, 1, 100}]
%t A194678 h[n_, k_] := f[p[n*r] + p[k*r]]
%t A194678 Flatten[Table[h[n, k], {n, 1, z}, {k, 1, n}]]
%t A194678  (* A194677 *)
%t A194678 TableForm[Table[h[n, k], {n, 1, z}, {k, 1, n}]]
%t A194678 t[n_] := Sum[h[n, k], {k, 1, n}]
%t A194678 Table[t[n], {n, 1, 100}]  (* A194678 *)
%Y A194678 Cf. A194677.
%K A194678 nonn
%O A194678 1,4
%A A194678 _Clark Kimberling_, Sep 01 2011