A194671
Number of k in [1,n] for which + > 1, where < > = fractional part and r = sqrt(5); row sums of A164670.
0, 0, 2, 4, 1, 2, 5, 8, 2, 4, 7, 11, 1, 4, 8, 13, 0, 4, 8, 14, 20, 4, 9, 16, 23, 4, 10, 17, 25, 2, 9, 17, 26, 0, 8, 16, 26, 36, 7, 16, 27, 38, 6, 16, 28, 40, 4, 15, 27, 40, 1, 13, 26, 40, 54, 12, 25, 40, 55, 10, 24, 40, 56, 7, 22, 38, 55, 3, 19, 36, 54, 72, 17, 34, 53, 72
Offset: 1
Keywords
Crossrefs
Cf. A194670.
Programs
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Mathematica
r = Sqrt[5]; z = 13; p[x_] := FractionalPart[x]; f[x_] := Floor[x]; w[n_, k_] := p[r^n] + p[r^k] - p[r^n + r^k] Flatten[Table[w[n, k], {n, 1, z}, {k, 1, n}]] TableForm[Table[w[n, k], {n, 1, z}, {k, 1, n}]] s[n_] := Sum[w[n, k], {k, 1, n}] (* A194669 *) Table[s[n], {n, 1, 100}] h[n_, k_] := f[p[n*r] + p[k*r]] Flatten[Table[h[n, k], {n, 1, z}, {k, 1, n}]] (* A194670 *) TableForm[Table[h[n, k], {n, 1, z}, {k, 1, n}]] t[n_] := Sum[h[n, k], {k, 1, n}] Table[t[n], {n, 1, 100}] (* A194671 *)