

A057117


Permutation of nonnegative integers obtained by mapping each forest of A000108[n] rooted binary plane trees from breadthfirst to depthfirst 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
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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..(n1))+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



