cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A069772 Self-inverse permutation of natural numbers induced by the automorphism xReflectHandshakes acting on the parenthesizations encoded by A014486.

Original entry on oeis.org

0, 1, 2, 3, 7, 6, 5, 4, 8, 9, 10, 21, 20, 19, 14, 15, 18, 17, 16, 13, 12, 11, 22, 45, 46, 44, 42, 43, 31, 32, 30, 28, 29, 63, 62, 61, 60, 54, 55, 53, 51, 52, 26, 27, 25, 23, 24, 59, 58, 57, 56, 40, 41, 39, 37, 38, 50, 49, 48, 47, 36, 35, 34, 33, 64, 65, 67, 66, 68, 69, 170
Offset: 0

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Author

Antti Karttunen, Apr 16 2002

Keywords

Comments

This automorphism reflects over the x-axis the interpretation n (the non-crossing handshakes) of Stanley's exercise 19.
Note that DeepRev (A057164) reflects over y-axis.
This transformation keeps palindromic parenthesizations/Dyck paths/rooted planar trees palindromic, but not necessarily same, meaning that this induces a permutation on the sequence A061855 (= A069766).

Links

Crossrefs

Composition of A057164 and A069771 in either order, i.e. A069772(n) = A057164(A069771(n)) = A069771(A057164(n)). Cf. also A061855, A069766, A057501, A069888, A069889.

A061855 Symmetric totally balanced binary sequences: those terms of A014486 which are equal to their reversed complement.

Original entry on oeis.org

0, 2, 10, 12, 42, 52, 56, 170, 178, 204, 212, 232, 240, 682, 722, 738, 812, 852, 868, 920, 936, 976, 992, 2730, 2762, 2866, 2898, 2978, 3010, 3244, 3276, 3380, 3412, 3492, 3524, 3640, 3672, 3752, 3784, 3888, 3920, 4000, 4032, 10922, 11082, 11146
Offset: 0

Views

Author

Antti Karttunen, May 11 2001

Keywords

Comments

These encode symmetric (palindromic) structures in many of the Catalan families, e.g. mountain ranges, parenthesizations, unlabeled rooted plane trees.

Examples

			E.g. the 45th term 11146 is 10101110001010 in binary and can be interpreted as a parenthesization: ( )( )((( )))( )( )

Links

Crossrefs

Obtained by "reflecting" the terms of A061854. Cf. also A035928 (ReflectBinSeq), A061856, A069766.

Programs

  • Maple
    map(op,[seq(PalTotBalBinSequences(j),j=1..10)]);
PalTotBalBinSequences := n -> map(ReflectBinSeq,NonDivingLatticeSequences(n), n);

Formula

a(0) = 0 and the rest with the Maple function map(op, [seq(PalTotBalBinSequences(j), j=1..10)]);
Showing 1-2 of 2 results.

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