A190363 a(n) = n + [n*r/t] + [n*s/t]; r=1, s=sqrt(5/4), t=sqrt(4/5).

3, 6, 9, 13, 16, 19, 22, 26, 30, 33, 36, 40, 43, 46, 49, 53, 57, 60, 63, 67, 70, 73, 76, 80, 83, 87, 90, 94, 97, 100, 103, 107, 110, 114, 117, 121, 124, 127, 130, 134, 137, 140, 144, 148, 151, 154, 157, 161, 164, 167, 171, 175, 178, 181, 184, 188, 191, 194, 197, 202, 205, 208, 211, 215, 218, 221, 224, 229, 232, 235, 238, 242, 245, 248

Offset

1,1

Comments

See A190361.

Conjecture: linear recurrence with constant coefficients 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1. - Harvey P. Dale, Jan 28 2025

Links

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

Formula

A190361: f(n) = n + [n*sqrt(5/4)] + [n*sqrt(4/5)].

A190362: g(n) = n + [n*sqrt(4/5)] + [4*n/5].

A190363: h(n) = 2*n + [n*sqrt(5/4)] + [n/4].

Mathematica

r=1; s=(5/4)^(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}]  (* A190361 *)
Table[g[n], {n, 1, 120}]  (* A190362 *)
Table[h[n], {n, 1, 120}]  (* A190363 *)
Table[n+Floor[n 1/Sqrt[4/5]]+Floor[n Sqrt[5/4]/Sqrt[4/5]], {n, 100}] (* Harvey P. Dale, Jan 28 2025 *)

Prog

(PARI) for(n=1, 100, print1(2*n + floor(n*sqrt(5/4)) + floor(n/4), ", ")) \\ G. C. Greubel, Apr 05 2018
(Magma) [2*n + Floor(n*Sqrt(5/4)) + Floor(n/4): n in [1..100]]; // G. C. Greubel, Apr 05 2018

Crossrefs

Cf. A190361, A190362.

Sequence in context: A198264 A186516 A059540 * A379408 A059550 A080081

Adjacent sequences: A190360 A190361 A190362 * A190364 A190365 A190366

Keyword

nonn

Author

Clark Kimberling, May 09 2011

Status

approved