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 A088208 Table read by rows where T(0,0)=1; n-th row has 2^n terms T(n,j),j=0 to 2^n-1. For j==0 mod 2, T(n+1,2j)=T(n,j) and T(n+1,2j+1)=T(n,j)+2^n. For j==1 mod 2, T(n+1,2j+1)=T(n,j) and T(n+1,2j)=T(n,j)+2^n. 4

%I

%S 1,1,2,1,3,4,2,1,5,7,3,4,8,6,2,1,9,13,5,7,15,11,3,4,12,16,8,6,14,10,2,

%T 1,17,25,9,13,29,21,5,7,23,31,15,11,27,19,3,4,20,28,12,16,32,24,8,6,

%U 22,30,14,10,26,18,2,1,33,49,17,25,57,41,9,13,45,61,29,21,53,37,5,7,39,55,23

%N Table read by rows where T(0,0)=1; n-th row has 2^n terms T(n,j),j=0 to 2^n-1. For j==0 mod 2, T(n+1,2j)=T(n,j) and T(n+1,2j+1)=T(n,j)+2^n. For j==1 mod 2, T(n+1,2j+1)=T(n,j) and T(n+1,2j)=T(n,j)+2^n.

%C Schroeder, p. 281 states "The ordering with which the iterates x_n fall into the 2^m different chaos bands [order as to magnitude] is also the same as the ordering of the iterates in a stable orbit of period length P = 2^m. For example, for both the period-4 orbit and the four chaos bands, the iterates, starting with the largest iterate x_1, are ordered as follows: x_1 > x_3 > x_4 > x_2."

%D Manfred R. Schroeder, "Fractals, Chaos, Power Laws", W.H. Freeman, 1991, p. 282.

%H Reinhard Zumkeller, <a href="/A088208/b088208.txt">Rows n = 1..13 of triangle, flattened</a>

%e 1

%e 1 2

%e 1 3 4 2

%e 1 5 7 3 4 8 6 2

%e 1 9 13 5 7 15 11 3 4 12 16 8 6 14 10 2

%t nmax = 6;

%t T[_, 0] = 1; T[n_, j_] /; j == 2^n = n;

%t Do[Which[

%t EvenQ[j], T[n+1, 2j] = T[n, j]; T[n+1, 2j+1] = T[n, j] + 2^n,

%t OddQ[j], T[n+1, 2j+1] = T[n, j]; T[n+1, 2j] = T[n, j] + 2^n],

%t {n, 0, nmax}, {j, 0, 2^n-1}];

%t Table[T[n, j], {n, 0, nmax}, {j, 0, 2^n-1}] // Flatten (* _Jean-François Alcover_, Aug 03 2018 *)

%o a088208 n k = a088208_tabf !! (n-1) !! (k-1)

%o a088208_row n = a088208_tabf !! (n-1)

%o a088208_tabf = iterate f  where

%o f vs = (map (subtract 1) ws) ++ reverse ws where ws = map (* 2) vs

%o -- _Reinhard Zumkeller_, Mar 14 2015

%Y Cf. A088372.

%Y Cf. A049773.

%K nonn,tabf

%O 1,3

%A _Gary W. Adamson_, Sep 23 2003

%E Edited by _Ray Chandler_ and _N. J. A. Sloane_, Oct 08 2003

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Last modified May 17 16:03 EDT 2021. Contains 343980 sequences. (Running on oeis4.)