This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A160136 #22 Sep 10 2023 19:06:43
%S A160136 0,1,10,2,3,5,8,4,12,7,19,17,9,26,35,16,6,13,28,14,15,11,44,37,18,46,
%T A160136 55,20,21,23,53,22,30,25,64,62,27,71,80,34,24,31,73,32,33,29,89,82,36,
%U A160136 91,100,38,39,41,98,40,48,43,109,107,45,116,125,52,42,49,118,50,51,47,134
%N A160136 Lodumo_9 of Fibonacci numbers.
%C A160136 Permutation of nonnegative integers.
%C A160136 From _Michael De Vlieger_, Jan 21 2021: (Start)
%C A160136 The plot is governed by A001175(9) = 24 and is bifurcated into two trajectories that repeat a "constellation" of points we label "red" and "blue" so as to match the linked figures. We might group the terms in a(n) into two classes as to their residue r (mod 24). The red terms have n = r (mod 24) for r in {1, 2, 6, 10, 11, 13, 14, 18, 22, 23}, while the blue terms have r in {0, 3, 4, 5, 7, 8, 9, 12, 15, 16, 17, 19, 20, 21}.
%C A160136 There are 10 residues in the red constellation, and 14 residues in the blue constellation.
%C A160136 For red, we have the displacement a(n + 24) - a(n) = 45, thus the slope m_red = 15/8. For blue, we have the displacement a(n + 24) - a(n) = 18, thus the slope m_blue = 3/4.(End)
%H A160136 Michael De Vlieger, <a href="/A160136/b160136.txt">Table of n, a(n) for n = 0..9999</a>
%H A160136 Michael De Vlieger, <a href="/A160136/a160136.png">Plot (n, a(n)) for 1 <= n <=144</a> illustrating bifurcation into two rays color coded red and blue, and the effect of the Pisano number (mod 9) = 24.
%H A160136 Michael De Vlieger, <a href="/A160136/a160136_1.png">Plot (n, a(n)) for 1 <= n <= 24</a> with the 2 rays color coded red and blue, with coordinates of points labeled.
%H A160136 OEIS wiki, <a href="/wiki/Lodumo_transform">Lodumo transform</a>
%H A160136 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%H A160136 <a href="/index/Rec#order_36">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
%F A160136 a(n) = lod_9(A000045(n)).
%F A160136 a(n) = 2*a(n-24) - a(n-48) for n >= 48. - _Philippe Deléham_, Mar 09 2023
%F A160136 a(n) = a(n-12) + a(n-24) - a(n-36) for n >= 36. - _Ray Chandler_, Sep 10 2023
%t A160136 Block[{m = 9, s = Fibonacci[Range[120]]}, Nest[Append[#1, Block[{k = 1}, While[Nand[Mod[k, m] == Mod[s[[#2]], m], FreeQ[#1, k]], k++]; k]] & @@ {#, Length@ #} &, {0}, 120]] (* _Michael De Vlieger_, Jan 21 2021 *)
%Y A160136 Cf. A000045, A007887.
%K A160136 easy,nonn
%O A160136 0,3
%A A160136 _Philippe Deléham_, May 02 2009
%E A160136 Replaced second 18 by 118 - _R. J. Mathar_, May 03 2009