A194682
Number of k in [1,n] for which + > 1, where < > = fractional part, and r=3-sqrt(2); row sums of A164681.
1, 0, 2, 1, 5, 4, 1, 6, 2, 9, 5, 0, 8, 2, 11, 5, 16, 10, 2, 14, 6, 20, 11, 1, 16, 5, 22, 11, 29, 18, 5, 24, 11, 32, 19, 4, 26, 10, 34, 18, 1, 26, 8, 34, 16, 44, 26, 6, 35, 14, 45, 24, 2, 34, 11, 45, 22, 57, 34, 9, 45, 20, 58, 32, 5, 44, 16, 57, 29, 0, 42, 12, 55, 25, 70, 40
Offset: 1
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 1..5000
Crossrefs
Cf. A194681.
Programs
-
Mathematica
r = 3 - Sqrt[2]; z = 15; 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}]] (* A194679 *) TableForm[Table[w[n, k], {n, 1, z}, {k, 1, n}]] s[n_] := Sum[w[n, k], {k, 1, n}] (* A194680 *) 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}]] (* A194681 *) 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}] (* A194682 *) -
PARI
for(n=1, 50, print1(sum(k=1,n, floor(frac(n*(3-sqrt(2))) + frac(k*(3-sqrt(2))))), ", ")) \\ G. C. Greubel, Feb 08 2018