A184824 a(n) = n + floor(n*t) + floor(n/t) + floor(n/t^2), where t is the tetranacci constant.

2, 6, 9, 14, 17, 21, 24, 29, 32, 36, 39, 44, 47, 50, 54, 58, 61, 65, 69, 73, 76, 80, 84, 88, 91, 95, 100, 102, 106, 110, 114, 117, 121, 125, 129, 132, 136, 140, 144, 147, 152, 154, 158, 161, 166, 169, 173, 176, 181, 184, 188, 191, 196, 200, 203, 207, 210, 214, 217, 222, 225, 229, 232, 237, 240, 244, 248, 252, 255, 258, 262, 266, 269, 273, 277, 281, 284, 288, 292, 296, 300, 304, 307, 310, 314, 318, 322, 325, 329, 333, 337, 340, 345, 348, 352, 355, 359, 362, 366, 369, 374, 377, 381, 384, 389, 392, 396, 401, 404, 408

Offset

1,1

Comments

This is one of four sequences that partition the positive integers.

Given t is the tetranacci constant, then the following sequences are disjoint:

. A184823(n) = n + [n/t] + [n/t^2] + [n/t^3],

. A184824(n) = n + [n*t] + [n/t] + [n/t^2],

. A184825(n) = n + [n*t] + [n*t^2] + [n/t],

. A184826(n) = n + [n*t] + [n*t^2] + [n*t^3], where []=floor.

This is a special case of Clark Kimberling's results given in A184812.

Links

Table of n, a(n) for n=1..110.

Formula

Limit a(n)/n = t^2 = 3.7154951693276375317543272...

a(n) = n + floor(n*p/r) + floor(n*q/r) + floor(n*s/r), where p=t, q=t^2, r=t^3, s=t^4, and t is the tetranacci constant.

Example

 Let t be the tetranacci constant, then t^2 = 1 + t + 1/t + 1/t^2 and:
t = 1.92756197548..., t^2 = 3.71549516932..., t^3 = 7.16184720848..., t^4 = 13.8049043532...

Prog

 (PARI) {a(n)=local(t=real(polroots(1+x+x^2+x^3-x^4)[2])); n+floor(n*t)+floor(n/t)+floor(n/t^2)}

Crossrefs

Cf. A184823, A184825, A184826; A184812, A086088.

Sequence in context: A171866 A297833 A049508 * A184836 A327895 A373327

Adjacent sequences: A184821 A184822 A184823 * A184825 A184826 A184827

Keyword

nonn

Author

Paul D. Hanna, Jan 23 2011

Status

approved