%I
%S 1,1,0,0,0,0,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,1,1,1,1,1,1,1,1,1,1,
%T 1,1,0,0,0,0,0,0,0,1,0,1,0,0,1,0,0,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,
%U 0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,1,0,0,0,1,0,1,0,0,0,0,0,0,1
%N Triangular array: T(n,k)=[<e^n>+<e^k>], where [ ] = floor, < > = fractional part.
%C nth row sum gives number of k in [0,1] for which <e^n>+<e^k> > 1; see A194676.
%e First ten rows:
%e 1
%e 1 0
%e 0 0 0
%e 1 0 0 1
%e 1 0 0 1 0
%e 1 0 0 1 0 0
%e 1 1 0 1 1 1 1
%e 1 1 1 1 1 1 1 1
%e 0 0 0 0 0 0 0 1 0
%e 1 0 0 1 0 0 1 1 0 0
%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}]] (* 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. A194676.
%K nonn,tabl
%O 1
%A _Clark Kimberling_, Sep 01 2011
