

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

A. Karttunen, Gatomorphisms (Includes the complete Scheme program for computing this sequence)


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.


KEYWORD

nonn


AUTHOR



STATUS

approved



