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A194678 Number of k in [1,n] for which <n*e>+<k*e> > 1, where < > = fractional part; row sums of A164677. 6

%I

%S 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 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 27,11,53,38,22,5,49,33,15,62,45,27,8,57,39,19,71,52,32,11,66,46

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

%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. A194677.

%K nonn

%O 1,4

%A _Clark Kimberling_, Sep 01 2011

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Last modified September 21 23:55 EDT 2019. Contains 327286 sequences. (Running on oeis4.)