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.

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

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