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A184824 a(n) = n + floor(n*t) + floor(n/t) + floor(n/t^2), where t is the tetranacci constant. 4
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 (list; graph; refs; listen; history; text; internal format)
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 A096378

Adjacent sequences:  A184821 A184822 A184823 * A184825 A184826 A184827

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 23 2011

STATUS

approved

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Last modified December 2 11:34 EST 2021. Contains 349440 sequences. (Running on oeis4.)