A190334 a(n) = n + floor(n*r/t) + floor(n*s/t) where r=1, s=sqrt(3), t=1/s.

5, 11, 17, 22, 28, 34, 40, 45, 51, 57, 63, 68, 74, 80, 85, 91, 97, 103, 108, 114, 120, 126, 131, 137, 143, 149, 154, 160, 166, 171, 177, 183, 189, 194, 200, 206, 212, 217, 223, 229, 235, 240, 246, 252, 257, 263, 269, 275, 280, 286, 292, 298, 303, 309, 315, 320, 326, 332, 338, 343, 349, 355, 361, 366, 372, 378, 384, 389, 395, 401

Offset

1,1

Comments

See A190332.

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Formula

a(n) = 4*n + floor(n*sqrt(3)).

From Miko Labalan, Dec 17 2016: (Start)

a(n) = floor(n*(4+sqrt(3))) = 4*n + A022838(n);

For n > 0, a(n) = 6*floor(n*(sqrt(3)-1)) + 5*floor(n*(2-sqrt(3))) + 5;

a(0) = 0, a(n) = a(n - 1) + A022838(n) - A022838(n - 1) + 4.

(End)

Maple

r:=1: s:=sqrt(3): t:=1/s: seq(n+floor(n*r/t)+floor(n*s/t), n=1..70); # Muniru A Asiru, Apr 05 2018

Mathematica

r=1; s=3^(1/2); t=1/s;
f[n_] := n + Floor[n*s/r] + Floor[n*t/r];
g[n_] := n + Floor[n*r/s] + Floor[n*t/s];
h[n_] := n + Floor[n*r/t] + Floor[n*s/t];
Table[f[n], {n, 1, 120}]  (*A190332*)
Table[g[n], {n, 1, 120}]  (*A190333*)
Table[h[n], {n, 1, 120}]  (*A190334*)

Prog

(Magma) [4*n+Floor(n*Sqrt(3)): n in [1..60]]; // Vincenzo Librandi, Dec 18 2016
(PARI) for(n=1, 100, print1(4*n + floor(n*sqrt(3)), ", ")) \\ G. C. Greubel, Apr 04 2018

Crossrefs

Cf. A190332, A190333.

Sequence in context: A314220 A187387 A314221 * A314222 A314223 A314224

Adjacent sequences: A190331 A190332 A190333 * A190335 A190336 A190337

Keyword

nonn

Author

Clark Kimberling, May 08 2011

Status

approved