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A194682 Number of k in [1,n] for which <n*r>+<k*r> > 1, where < > = fractional part, and r=3-sqrt(2); row sums of A164681. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000

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 *)

PROG

(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

CROSSREFS

Cf. A194681.

Sequence in context: A171090 A141506 A271684 * A274105 A056242 A128718

Adjacent sequences:  A194679 A194680 A194681 * A194683 A194684 A194685

KEYWORD

nonn

AUTHOR

Clark Kimberling, Sep 01 2011

STATUS

approved

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Last modified June 5 12:47 EDT 2020. Contains 334840 sequences. (Running on oeis4.)