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Search: id:A057162
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| A057162 |
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Permutation of natural numbers induced by clockwise rotation of the triangularizations of polygons encoded by A014486. |
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+0
11
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| 0, 1, 3, 2, 8, 6, 7, 4, 5, 22, 19, 20, 14, 15, 21, 16, 17, 9, 10, 18, 11, 12, 13, 64, 60, 61, 51, 52, 62, 53, 54, 37, 38, 55, 39, 40, 41, 63, 56, 57, 42, 43, 58, 44, 45, 23, 24, 46, 25, 26, 27, 59, 47, 48, 28, 29, 49, 30, 31, 32, 50, 33, 34, 35, 36, 196, 191, 192, 177, 178
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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In A057161 and A057162, the cycles between A014138[n-1]+1-th and A014138[n]th term partition A000108[n] objects encoded by the corresponding terms of A014486 into A001683[n+2] equivalence classes of flexagons (or unlabeled plane boron trees), thus the latter sequence can be produced also with the Maple procedure RotBinTreePermutationCycleCounts given below.
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LINKS
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A. Karttunen, Table of n, a(n) for n = 0..2055
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(RotateTriangularizationR(A014486[n]))
RotateTriangularizationR := n -> ReflectBinTree(RotateTriangularization(ReflectBinTree(n)));
with(group); RotBinTreePermutationCycleCounts := proc(upto_n) local u, n, a, r, b; a := []; for n from 0 to upto_n do b := []; u := (binomial(2*n, n)/(n+1)); for r from 0 to u-1 do b := [op(b), 1+CatalanRank(n, RotateTriangularization(CatalanUnrank(n, r)))]; od; a := [op(a), (`if`((n < 2), 1, nops(convert(b, 'disjcyc'))))]; od; RETURN(a); end;
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PROGRAM
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(Scheme function implementing this automorphism on list-structures:) (define (RotateTriangularizationInv bt) (let loop ((lt bt) (nt (list))) (cond ((not (pair? lt)) nt) (else (loop (cdr lt) (cons nt (car lt)))))))
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CROSSREFS
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Inverse of A057161 and also its car/cdr-flipped conjugate, composition of A057508 & A069768, i.e. A057162(n) = A057163(A057161(A057163(n))) = A069768(A057508(n)).
Sequence in context: A089860 A130960 A130927 this_sequence A125982 A125983 A130364
Adjacent sequences: A057159 A057160 A057161 this_sequence A057163 A057164 A057165
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen Aug 18 2000
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