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A065626 Table of permutations of N, each row being a generator of the "rotation group" of infinite planar binary tree. Inverse generators are given in A065625. 9
2, 4, 1, 1, 4, 1, 8, 3, 2, 1, 9, 8, 6, 2, 1, 5, 2, 4, 3, 2, 1, 3, 6, 5, 8, 3, 2, 1, 16, 7, 12, 5, 4, 3, 2, 1, 17, 16, 3, 6, 10, 4, 3, 2, 1, 18, 17, 8, 7, 6, 5, 4, 3, 2, 1, 19, 9, 9, 16, 7, 12, 5, 4, 3, 2, 1, 10, 5, 10, 4, 8, 7, 6, 5, 4, 3, 2, 1, 11, 12, 11, 10, 9, 8, 14, 6, 5, 4, 3, 2, 1, 6, 13, 24, 11, 20, 9, 8, 7, 6, 5, 4, 3, 2, 1, 7, 14, 25, 12, 5, 10, 9, 16, 7, 6, 5, 4, 3, 2 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..118.

MAPLE

[seq(RotateLeftTable(j), j=0..119)];

RotateLeftTable := n -> RotateNodeLeft(1+(n-((trinv(n)*(trinv(n)-1))/2)), (((trinv(n)-1)*(((1/2)*trinv(n))+1))-n)+1);

# Rewrites t-prefixed x's in the following way: t -> t0, t0... -> t00..., t1 -> t, t10... -> t01..., t11... -> t1... and leaves other x's intact.

RotateNodeLeft := proc(t, x) local u, y; u := floor_log_2(t)+1; y := floor_log_2(x)+1; if(y < u) then RETURN(x); fi; if(floor(x/(2^(y-u))) <> t) then RETURN(x); fi; if(x = t) then RETURN(2*x); fi; if(0 = (floor(x/(2^(y-u-1))) mod 2)) then RETURN(x + (t * 2^(y-u))); fi; if(y = (u+1)) then RETURN((x-1)/2); fi; if(0 = (floor(x/(2^(y-u-2))) mod 2)) then RETURN(x - 2^(y-u-2)); fi; RETURN(x - ((t+1) * 2^(y-u-1))); end;

CROSSREFS

The first row (rotate the top node left): A057115, 2nd row (rotate the top node's left child): A065628, 3rd row (rotate the top node's right child): A065630, 4th row: A065632, 5th row: A065634, 6th row: A065636, 7th row: A065638, 8th row: A065640. Maple procedure floor_log_2 given in A054429, for trinv, follow A065167.

Sequence in context: A139227 A269750 A292495 * A201758 A096110 A207260

Adjacent sequences:  A065623 A065624 A065625 * A065627 A065628 A065629

KEYWORD

nonn,tabl

AUTHOR

Antti Karttunen, Nov 08 2001

STATUS

approved

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Last modified August 7 19:57 EDT 2020. Contains 336279 sequences. (Running on oeis4.)