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 A038776 The sequence a[1] to a[ cat[n] ] is the permutation that converts forest[n] of depth-first planar planted binary trees into breadth-first representation. 11
 1, 2, 4, 5, 3, 9, 10, 13, 14, 12, 6, 7, 8, 11, 23, 24, 27, 28, 26, 36, 37, 41, 42, 40, 32, 33, 35, 39, 15, 16, 18, 19, 17, 22, 25, 20, 21, 34, 38, 29, 30, 31, 65, 66, 69, 70, 68, 78, 79, 83, 84, 82, 74, 75, 77, 81, 106, 107, 111, 112, 110, 125, 126, 131, 132, 130 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS A. Karttunen, Table of n, a(n) for n = 1..1430 A. Karttunen, Gatomorphisms (Includes the complete Scheme program for computing this sequence) EXAMPLE tree ( 1 (100) (10 ) ) becomes (1) (11)(00 0 ) thus (1 (1(100) 0) ) and is permuted from position 3 in forest[3] to position 5 by permutation {1,2,4,5,3}={{1},{2},{4,5,3}} MAPLE [seq(CatalanRank(inf, (btbf2df(binrev(CatalanUnrank(inf, j)), 0, 1)/2))+1, j=0..(binomial(2*inf, inf)/(inf+1))-1)]; (In practice, use a value like 6 instead of infinity). btbf2df := proc(nn, i, r) local n, j, c, x, y, w; n := nn; if(0 = (n mod 2)) then RETURN(0); fi; c := i; for j from 1 to r do c := c + (n mod 2); n := floor(n/2); od; w := 2*c; c := 0; for j from 1 to (2*i) do c := c + (n mod 2); n := floor(n/2); od; x := btbf2df(n, c, (w-(j-1))); y := btbf2df(floor(n/2), c+(n mod 2), (w-(j))); RETURN((2^(binwidth(x)+binwidth(y))) + (x * (2^(binwidth(y)))) + y); end; floor_log_2 := proc(n) local nn, i: nn := n; for i from -1 to n do if(0 = nn) then RETURN(i); fi: nn := floor(nn/2); od: end: binwidth := n -> (`if`((0 = n), 1, floor_log_2(n)+1)); binrev := proc(nn) local n, z; n := nn; z := 0; while(n <> 0) do z := 2*z + (n mod 2); n := floor(n/2); od; RETURN(z); end; MATHEMATICA bracket[ tree_ ] := (Flatten[ {tree, 0} ]/. 0->{0})//.{1, z___, 1, a_List, b_List, y___}:>{1, z, {1, a, b}, y}; widthfirst[ dectree_ ] := b2d[ Drop[ Flatten[ {Table[ Cases[ Level[ #, {k}, z ], _Integer ], {k, Depth[ # ]-1} ] }/.z->List ], -1 ] ] & @(bracket@d2b[ dectree ]); ToCycles[ Ordering[ widthfirst/@wood[ 9 ] ] ]; compare functions in A014486. CROSSREFS Compare to the plot of A082364 and A072619. Inverse of A070041. Cf. also A038774, A038775. If "expanded" produces A057117. Max cycle lengths: A057542. Sequence in context: A060736 A097292 A269780 * A210863 A245816 A118461 Adjacent sequences:  A038773 A038774 A038775 * A038777 A038778 A038779 KEYWORD nonn AUTHOR Wouter Meeussen, May 04 2000 EXTENSIONS Additional comments from Antti Karttunen, Aug 11 2000 STATUS approved

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Last modified October 15 20:04 EDT 2019. Contains 328037 sequences. (Running on oeis4.)