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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
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, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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."

REFERENCES

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

LINKS

Reinhard Zumkeller, Rows n = 1..13 of triangle, flattened

EXAMPLE

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

PROG

(Haskell)

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

a088208_row n = a088208_tabf !! (n-1)

a088208_tabf = iterate f [1] where

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

-- Reinhard Zumkeller, Mar 14 2015

CROSSREFS

Cf. A088372.

Cf. A049773.

Sequence in context: A248514 A123390 A162598 * A081878 A088606 A140073

Adjacent sequences:  A088205 A088206 A088207 * A088209 A088210 A088211

KEYWORD

nonn,tabf

AUTHOR

Gary W. Adamson, Sep 23 2003

EXTENSIONS

Edited by Ray Chandler and N. J. A. Sloane, Oct 08 2003

STATUS

approved

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Last modified August 18 14:06 EDT 2017. Contains 290720 sequences.