%I A060118
%S A060118 1,2,1,1,3,2,2,3,1,3,2,1,3,1,2,1,2,4,3,2,1,4,3,1,3,4,2,2,3,4,1,3,2,4,1,
%T A060118 3,1,4,2,1,4,3,2,2,4,3,1,1,4,2,3,2,4,1,3,3,4,1,2,3,4,2,1,4,2,3,1,4,1,3,
%U A060118 2,4,3,2,1,4,3,1,2,4,2,1,3,4,1,2,3,1,2,3,5,4,2,1,3,5,4,1,3,2,5,4,2,3,1
%N A060118 A list of all finite permutations in "PermUnrank3L" ordering. (Inverses 
               of the permutations of A060117).
%C A060118 In contrast to PermUnrank3R (A060117), PermUnrank3L applies each successive 
               transposition from the left, not from the right, thus producing the 
               inverse (permutation) of what PermUnrank3R would produce.
%F A060118 [seq(op(PermUnrank3L(j)), j=0..)]; (Maple code given below)
%e A060118 In this table each row consists of A001563[n] permutations of (n+1) terms;
%e A060118 Append to each an infinite amount of fixed terms and we get a list of 
               rearrangements of natural numbers, but with only a finite number 
               of terms permuted:
%e A060118 1/2,3,4,5,6,7,8,9,...
%e A060118 2,1/3,4,5,6,7,8,9,...
%e A060118 1,3,2/4,5,6,7,8,9,...
%e A060118 2,3,1/4,5,6,7,8,9,...
%e A060118 3,2,1/4,5,6,7,8,9,...
%e A060118 3,1,2/4,5,6,7,8,9,...
%e A060118 1,2,4,3/5,6,7,8,9,...
%e A060118 2,1,4,3/5,6,7,8,9,...
%p A060118 with(group); permul := (a,b) -> mulperms(b,a); PermUnrank3L := proc(r) 
               local n; n := nops(factorial_base(r)); convert(PermUnrank3Laux(n+1,
               r,[]),'permlist',1+(((r+2) mod (r+1))*n)); end; PermUnrank3Laux := 
               proc(n,r,p) local s; if(0 = r) then RETURN(p); else s := floor(r/
               ((n-1)!)); RETURN(PermUnrank3Laux(n-1, r-(s*((n-1)!)), permul([[n,
               n-s]],p))); fi; end;
%Y A060118 A060120 = Positions of these permutations in the "canonical list" A055089. 
               Cf. also A060117.
%Y A060118 Sequence in context: A120643 A111867 A133776 this_sequence A029308 A029259 
               A159266
%Y A060118 Adjacent sequences: A060115 A060116 A060117 this_sequence A060119 A060120 
               A060121
%K A060118 nonn
%O A060118 0,2
%A A060118 Antti Karttunen Mar 02 2001