A194662 - OEIS

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.

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, 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, 35, 13, 50, 28, 5, 43, 20, 60, 37, 12, 53, 28, 2, 45, 18, 63, 36, 8, 54, 26, 74, 46

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OFFSET

1,3

LINKS

Table of n, a(n) for n=1..77.

MATHEMATICA

r = GoldenRatio; z = 14;

p[x_] := FractionalPart[x]; f[x_] := Floor[x];

h[n_, k_] := f[p[n*r] + p[k*r]]

Flatten[Table[h[n, k], {n, 1, z}, {k, 1, n}]] (* A194661 *)

TableForm[Table[h[n, k], {n, 1, z}, {k, 1, n}]]

t[n_] := Sum[h[n, k], {k, 1, n}]