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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A122351 Row 1 of A122289 and A122290. An involution of nonnegative integers.

Original entry on oeis.org

0, 1, 3, 2, 7, 8, 6, 4, 5, 18, 17, 20, 22, 21, 16, 19, 14, 10, 9, 15, 11, 13, 12, 49, 50, 48, 45, 46, 55, 54, 61, 63, 64, 57, 62, 58, 59, 47, 44, 53, 60, 56, 42, 51, 38, 26, 27, 37, 25, 23, 24, 43, 52, 39, 29, 28, 41, 33, 35, 36, 40, 30, 34, 31, 32, 143, 142, 146, 148, 147
Offset: 0

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Author

Antti Karttunen, Sep 01 2006

Keywords

Comments

The signature-permutation of the automorphism which is derived from the automorphism *A057163 with the recursion schema FORK (see A122201), that is, from the first non-recursive automorphism *A069770 with FORK(FORK(*A069770)) or equivalently, with KROF(KROF(*A069770)) (see A122202).

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Crossrefs

A007595 gives the number of orbits in range [A014137(n-1)..A014138(n-1)] of this permutation.

A129604 Signature-permutation of a Catalan automorphism, row 1654720 of A089840.

Original entry on oeis.org

0, 1, 3, 2, 8, 7, 6, 5, 4, 21, 22, 20, 17, 18, 19, 16, 15, 12, 13, 14, 11, 9, 10, 58, 59, 62, 63, 64, 57, 61, 54, 45, 46, 55, 48, 49, 50, 56, 60, 53, 44, 47, 52, 43, 40, 31, 32, 41, 34, 35, 36, 51, 42, 39, 30, 33, 37, 28, 23, 24, 38, 29, 25, 26, 27, 170, 171, 174, 175, 176
Offset: 0

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Author

Antti Karttunen, May 22 2007

Keywords

Comments

This involution effects the following transformation on the binary trees (labels A,B,C,D refer to arbitrary subtrees located on those nodes and () stands for a terminal node.)
.A..B.C..D.....D..C.B..A.......B...C...C...B........A...B............B...A
..\./.\./.......\./.\./.........\./.....\./..........\./..............\./.
...x...x....-->..x...x.......()..x..-->..x..()........x..()...-->..()..x..
....\./...........\./.........\./.........\./..........\./..........\./...
.....x.............x...........x...........x............x............x....
Note that automorphism *A069770 = FORK(*A129604) = KROF(*A129604). See the definitions given in A122201 and A122202.

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Crossrefs

a(n) = A069770(A089864(n)) = A089864(A069770(n)). The number of cycles and the number of fixed points in range [A014137(n-1)..A014138(n-1)] of this involution are given by the same sequences as is the case for example with A069770, A057163 and A122351, that is, A007595 and zero-interspersed A000108.

A130924 Signature permutation of a Catalan automorphism: Inverse KROF-transform of automorphism *A120706.

Original entry on oeis.org

0, 1, 3, 2, 7, 6, 8, 4, 5, 17, 18, 15, 14, 16, 20, 19, 21, 9, 10, 22, 11, 12, 13, 48, 46, 50, 49, 45, 40, 39, 41, 37, 38, 43, 42, 44, 47, 54, 55, 52, 51, 53, 57, 56, 58, 23, 24, 59, 25, 26, 27, 61, 60, 62, 28, 29, 63, 30, 31, 32, 64, 33, 34, 35, 36, 141, 145, 134, 133, 139
Offset: 0

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Author

Antti Karttunen, Jun 11 2007

Keywords

Comments

This is the unique Catalan automorphism f, such that *A120706 = (KROF f). See A122202 for the definition of KROF.

Links

Crossrefs

Inverse: A130923. Cf. A130925 & A130926.

A130926 Signature permutation of a Catalan automorphism: Inverse KROF-transform of automorphism *A120705.

Original entry on oeis.org

0, 1, 3, 2, 7, 8, 4, 6, 5, 17, 18, 20, 21, 22, 9, 10, 14, 15, 19, 11, 16, 12, 13, 45, 46, 48, 49, 50, 54, 55, 57, 58, 59, 61, 62, 63, 64, 23, 24, 25, 26, 27, 37, 38, 39, 40, 41, 51, 52, 56, 60, 28, 29, 42, 43, 44, 30, 53, 36, 32, 33, 47, 31, 35, 34, 129, 130, 132, 133, 134
Offset: 0

Views

Author

Antti Karttunen, Jun 11 2007

Keywords

Comments

This is the unique Catalan automorphism f, such that *A120705 = (KROF f). See A122202 for the definition of KROF.

Links

Crossrefs

Inverse: A130925. Cf. A130923 & A130924.

A122364 Row 2 of A122290.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 5, 7, 8, 9, 10, 14, 16, 19, 11, 15, 12, 17, 18, 13, 20, 21, 22, 23, 37, 25, 26, 27, 24, 38, 42, 44, 53, 51, 47, 56, 60, 28, 29, 39, 43, 52, 30, 40, 31, 45, 54, 32, 48, 49, 50, 33, 41, 34, 46, 55, 35, 57, 58, 62, 36, 61, 59, 63, 64, 65, 70, 66, 121, 149, 107
Offset: 0

Views

Author

Antti Karttunen, Sep 01 2006

Keywords

Comments

The signature-permutation of the automorphism which is derived from the second non-recursive automorphism *A072796 with KROF(KROF(*A072796)) = KROF(*A057512). (see A122202 for the definition of KROF).

Links

Crossrefs

Inverse: A122363.
Previous Showing 31-35 of 35 results.

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