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Search: id:A057117
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| A057117 |
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Permutation of nonnegative integers obtained by mapping each forest of A000108[n] rooted binary plane trees from breadth-first to depth-first encoding. |
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18
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| 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; listen)
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OFFSET
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0,3
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LINKS
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A. Karttunen, Gatomorphisms (Includes the complete Scheme program for computing this sequence)
Index entries for sequences that are permutations of the natural numbers
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MAPLE
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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;
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CROSSREFS
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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 this_sequence A130941 A082360 A130392
Adjacent sequences: A057114 A057115 A057116 this_sequence A057118 A057119 A057120
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen Aug 11 2000
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