login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A190509 a(n) = n + [nr/s] + [nt/s] + [nu/s] where r=golden ratio, s=r^2, t=r^3, u=r^4, and [] represents the floor function. 4
4, 11, 15, 22, 29, 33, 40, 44, 51, 58, 62, 69, 76, 80, 87, 91, 98, 105, 109, 116, 120, 127, 134, 138, 145, 152, 156, 163, 167, 174, 181, 185, 192, 199, 203, 210, 214, 221, 228, 232, 239, 243, 250, 257, 261, 268, 275, 279, 286, 290, 297, 304, 308, 315, 319, 326, 333, 337, 344, 351, 355, 362, 366, 373, 380, 384, 391, 398, 402, 409 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A190508.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Weiru Chen, Jared Krandel, Interpolating Classical Partitions of the Set of Positive Integers, arXiv:1810.11938 [math.NT], 2018. See sequence D1 p. 4.

FORMULA

A190508: a(n) = n + [nr] + [nr^2] + [nr^3];

A190509: b(n) = [n/r] + n + [nr] + [nr^2];

A054770: c(n) = [n/r^2] + [n/r] + n + [nr];

A190511: d(n) = [n/r^3] + [n/r^2] + [n/r] + n.

a(n) = 3*A000201(n)+n, since r/s = 1/r = r-1, and u/s = r^2 = r+1 - Michel Dekking, Sep 06 2017

MAPLE

r:=(1+sqrt(5))/2: s:=r^2: t:=r^3: u:=r^4: a:=n->n+floor(n*r/s)+floor(n*t/s)+floor(n*u/s):  seq(a(n), n=1..70); # Muniru A Asiru, Nov 01 2018

MATHEMATICA

(See A190508.)

Table[3 Floor[n (Sqrt[5] + 1) / 2] + n, {n, 1, 100}] (* Vincenzo Librandi, Nov 01 2018 *)

PROG

(PARI) a(n) = 3*floor(n*(sqrt(5)+1)/2) + n; \\ Michel Marcus, Sep 10 2017; after Michel Dekking's formula

(MAGMA) [3*Floor(n*(Sqrt(5)+1)/2) + n: n in [1..80]]; // Vincenzo Librandi, Nov 01 2018

CROSSREFS

Cf. A054770, A190508, A190511.

Sequence in context: A288316 A003250 A320494 * A022131 A091391 A135105

Adjacent sequences:  A190506 A190507 A190508 * A190510 A190511 A190512

KEYWORD

nonn

AUTHOR

Clark Kimberling, May 11 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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 21 00:13 EST 2019. Contains 329348 sequences. (Running on oeis4.)