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 A057117 Permutation of nonnegative integers obtained by mapping each forest of A000108[n] rooted binary plane trees from breadth-first to depth-first encoding. 18
 0, 1, 2, 3, 4, 5, 7, 8, 6, 9, 10, 12, 13, 11, 17, 18, 21, 22, 20, 14, 15, 16, 19, 23, 24, 26, 27, 25, 31, 32, 35, 36, 34, 28, 29, 30, 33, 45, 46, 49, 50, 48, 58, 59, 63, 64, 62, 54, 55, 57, 61, 37, 38, 40, 41, 39, 44, 47, 42, 43, 56, 60, 51, 52, 53, 65, 66, 68, 69, 67, 73, 74 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..71. A. Karttunen, Gatomorphisms (Includes the complete Scheme program for computing this sequence) Index entries for sequences that are permutations of the natural numbers MAPLE a(n) = CatalanRankGlobal(btbf2df(binrev(A014486[n]), 0, 1)/2) Maple procedure CatalanRank is adapted from the algorithm 3.23 of the CAGES book, see A014486 CatalanRank := proc(n, aa) local x, y, lo, a; a := binrev(aa); y := 0; lo := 0; for x from 1 to (2*n)-1 do lo := lo + (1-(a mod 2))*Mn(n, x, y+1); y := y - ((-1)^a); a := floor(a/2); od; RETURN((binomial(2*n, n)/(n+1))-(lo+1)); end; CatalanRankGlobal := proc(a) local n; n := floor(binwidth(a)/2); RETURN(add((binomial(2*j, j)/(j+1)), j=0..(n-1))+CatalanRank(n, a)); end; CROSSREFS Restriction of the automorphism A072088 to the plane binary trees. Add one to each term and "overlay" each successive subpermutation of A000108[n] terms and one obtains A038776. Inverse permutation is A057118. Sequence in context: A130349 A130354 A082356 * A130941 A082360 A130392 Adjacent sequences: A057114 A057115 A057116 * A057118 A057119 A057120 KEYWORD nonn AUTHOR Antti Karttunen, Aug 11 2000 STATUS approved

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Last modified August 14 05:24 EDT 2024. Contains 375146 sequences. (Running on oeis4.)