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%I #5 Mar 30 2012 18:57:43
%S 1,1,0,2,2,2,6,8,1,4,1,9,4,3,4,6,14,1,19,7,8,2,4,19,7,21,22,10,2,10,
%T 10,24,2,30,27,7,11,7,38,14,8,13,14,37,0,4,12,15,3,15,4,35,38,15,26,5,
%U 45,53,17,17,4,1,12,60,19,3,20,20,50,5,48,22,47,66,0,75,73,27,25
%N Number of k in [1,n] for which <e^n>+<e^k> > 1, where < > = fractional part.
%t r = E; z = 15;
%t p[x_] := FractionalPart[x]; f[x_] := Floor[x];
%t w[n_, k_] := p[r^n] + p[r^k] - p[r^n + r^k]
%t Flatten[Table[w[n, k], {n, 1, z}, {k, 1, n}]]
%t (* A194675 *)
%t TableForm[Table[w[n, k], {n, 1, z}, {k, 1, n}]]
%t s[n_] := Sum[w[n, k], {k, 1, n}] (* A194676 *)
%t Table[s[n], {n, 1, 100}]
%t h[n_, k_] := f[p[n*r] + p[k*r]]
%t Flatten[Table[h[n, k], {n, 1, z}, {k, 1, n}]]
%t (* A194677 *)
%t TableForm[Table[h[n, k], {n, 1, z}, {k, 1, n}]]
%t t[n_] := Sum[h[n, k], {k, 1, n}]
%t Table[t[n], {n, 1, 100}] (* A194678 *)
%Y Cf. A194675.
%K nonn
%O 1,4
%A _Clark Kimberling_, Sep 01 2011
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