The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A194682 Number of k in [1,n] for which + > 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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