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A184826 a(n) = n + floor(n*t) + floor(n*t^2) + floor(n*t^3) where t is the tetranacci constant. 4
12, 26, 40, 53, 67, 81, 96, 109, 123, 137, 150, 164, 179, 192, 205, 219, 233, 246, 261, 275, 289, 302, 316, 330, 344, 358, 372, 385, 398, 412, 427, 440, 454, 468, 482, 495, 509, 524, 537, 551, 565, 578, 591, 606, 620, 633, 647, 661, 675, 689, 703, 717, 730, 744, 758, 772, 785, 799, 813, 826, 840, 855, 869, 882, 896, 910, 923, 938, 952, 965, 978, 992, 1006, 1019, 1034, 1048, 1062, 1075, 1089, 1103, 1117, 1131, 1144, 1158, 1171, 1185, 1200, 1213, 1227, 1241, 1255, 1268, 1283, 1297, 1310, 1324, 1337, 1351 (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..98.

FORMULA

Limit a(n)/n = t^4 = 13.804904353297009893939920...

a(n) = n + floor(n*q/p) + floor(n*r/p) + floor(n*s/p), 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^4 = 1 + t + t^2 + t^3 and:

t = 1.92756197548..., t^2 = 3.71549516932..., t^3 = 7.16184720848..., t^4 = 13.8049043532...

MATHEMATICA

Module[{t=x/.FindRoot[x^4-x^3-x^2-x-1==0, {x, 2}, WorkingPrecision->200], t2, t3}, t2=t^2; t3=t^3; Table[n+Floor[t*n]+Floor[t2*n]+Floor[t3*n], {n, 100}]] (* Harvey P. Dale, Oct 18 2012 *)

PROG

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

CROSSREFS

Cf. A184823, A184824, A184825; A184812, A086088.

Sequence in context: A025138 A075689 A054303 * A119412 A105814 A297427

Adjacent sequences:  A184823 A184824 A184825 * A184827 A184828 A184829

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 23 2011

STATUS

approved

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Last modified August 8 23:02 EDT 2020. Contains 336300 sequences. (Running on oeis4.)