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A065626
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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.
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9
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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; internal format)
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OFFSET
| 0,1
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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;
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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: A194524 A117136 A139227 * A201758 A096110 A187913
Adjacent sequences: A065623 A065624 A065625 * A065627 A065628 A065629
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KEYWORD
| nonn,tabl
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AUTHOR
| Antti Karttunen Nov 08 2001
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