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.

Showing 1-6 of 6 results.

A127388 Signature-permutation of a Catalan automorphism, a self-inverse variant of A127379.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 8, 7, 9, 10, 11, 13, 12, 14, 15, 19, 22, 21, 16, 20, 18, 17, 23, 24, 25, 27, 26, 28, 29, 33, 36, 35, 30, 34, 32, 31, 37, 38, 39, 41, 40, 51, 52, 60, 64, 63, 56, 62, 59, 58, 42, 43, 53, 54, 55, 47, 61, 50, 49, 44, 57, 48, 46, 45, 65, 66, 67, 69, 68, 70, 71
Offset: 0

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Author

Antti Karttunen, Jan 16 2007

Keywords

Comments

This automorphism is RIBS-transformation (explained in A122200) of the automorphism A127387.

Links

Crossrefs

The number of cycles and the number of fixed points in range [A014137(n-1)..A014138(n-1)] of this involution are given by A127386 and A086625 shifted once right (this automorphism has the same fixed points as A127379/A127380). A127302(a(n)) = A127302(n) holds for all n.

A127384 Number of cycles in range [A014137(n-1)..A014138(n-1)] of permutations A127379/A127380 and A127381/A127382.

Original entry on oeis.org

1, 1, 2, 4, 9, 23, 62, 179, 543, 1705, 5482, 18056, 60634, 206824
Offset: 0

Views

Author

Antti Karttunen, Jan 16 2007

Keywords

Links

Crossrefs

A127383.

A127377 Signature-permutation of a Catalan automorphism, auxiliary bijection for Callan's 2006 bijection on Dyck Paths.

Original entry on oeis.org

0, 1, 3, 2, 8, 7, 6, 4, 5, 22, 21, 20, 17, 18, 14, 15, 19, 9, 10, 16, 11, 13, 12, 64, 63, 62, 58, 59, 54, 55, 61, 45, 46, 57, 48, 50, 49, 37, 38, 39, 41, 40, 51, 52, 60, 23, 24, 56, 25, 27, 26, 42, 43, 53, 28, 29, 44, 33, 36, 35, 47, 30, 34, 31, 32, 196, 195, 194, 189, 190
Offset: 0

Views

Author

Antti Karttunen, Jan 16 2007

Keywords

Comments

Used to construct A127379.

Links

Crossrefs

Inverse: A127378. The number of cycles and the number of fixed points in range [A014137(n-1)..A014138(n-1)] of this permutation are given by A127383 and A127389. The maximum cycles and LCM's of cycle sizes begin as 1, 1, 2, 4, 4, 8, 8, 8, 8, 16, 16, 16, 16, 16, ... A127387 shows a variant which is an involution. A127302(a(n)) = A127302(n) holds for all n.

A127380 Signature-permutation of the inverse of Callan's 2006 bijection on Dyck Paths, mirrored version (A057164-conjugate).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 8, 7, 9, 10, 11, 13, 12, 14, 15, 19, 21, 22, 16, 20, 18, 17, 23, 24, 25, 27, 26, 28, 29, 33, 35, 36, 30, 34, 32, 31, 37, 38, 39, 41, 40, 51, 52, 56, 58, 59, 60, 62, 64, 63, 42, 43, 53, 54, 55, 47, 61, 49, 50, 44, 57, 48, 46, 45, 65, 66, 67, 69, 68, 70, 71
Offset: 0

Views

Author

Antti Karttunen, Jan 16 2007

Keywords

Comments

This automorphism is RIBS-transformation (explained in A122200) of the automorphism A127378 and Callan's original variant A127382 is obtained as A057164(A127380(A057164(n))).

Links

Crossrefs

Inverse: A127379. a(n) = A057164(A127382(A057164(n))). A127302(a(n)) = A127302(n) holds for all n.
Differs from A073288 for the first time at n=49, where a(n)=64, while A073288(49)=63 and differs from A122350 for the first time at n=54, where a(n)=54, while A122350(54)=57.

A127381 Signature-permutation of Callan's 2006 bijection on Dyck Paths.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 8, 7, 9, 10, 11, 13, 12, 14, 15, 19, 22, 18, 16, 21, 17, 20, 23, 24, 25, 27, 26, 28, 29, 33, 36, 32, 30, 35, 31, 34, 37, 38, 39, 41, 40, 51, 52, 60, 64, 46, 47, 59, 50, 49, 42, 43, 56, 63, 55, 44, 58, 45, 48, 53, 62, 54, 61, 57, 65, 66, 67, 69, 68, 70, 71
Offset: 0

Views

Author

Antti Karttunen, Jan 16 2007

Keywords

Comments

This automorphism is much easier to implement for S-expressions when viewed as a A057164-conjugate of A127379. See the comments in the latter entry.

Links

Crossrefs

Inverse: A127382. a(n) = A057164(A127379(A057164(n))). The number of cycles and the number of fixed points in range [A014137(n-1)..A014138(n-1)] of this permutation are given by A127384 and A086625 shifted once right. The maximum cycles and LCM's of cycle sizes begin as 1, 1, 1, 2, 4, 4, 8, 8, 8, 8, 16, 16, 16, 16, ...

A153247 Number of fleeing trees computed for Catalan bijection A123493.

Original entry on oeis.org

0, 0, 1, 1, 2, 1, 0, 2, 1, 3, 2, 0, 2, 1, 3, 1, 3, 3, 2, 1, 0, 2, 1, 4, 3, 1, 3, 2, 3, 1, 3, 3, 2, 1, 0, 2, 1, 4, 3, 0, 2, 1, 2, 2, 4, 4, 3, 3, 1, 3, 2, 2, 2, 0, 3, 1, 2, 3, 3, 2, 1, 1, 0, 2, 1, 5, 4, 2, 4, 3, 4, 2, 4, 4, 3, 2, 1, 3, 2, 4, 3, 0, 2, 1, 2, 2, 4, 4, 3, 3, 1, 3, 2, 2, 2, 0, 3, 1, 2, 3, 3, 2
Offset: 0

Views

Author

Antti Karttunen, Dec 22 2008

Keywords

Comments

See comments at A153246. Essentially, A123493 does not extend uniquely to an automorphism of infinite binary tree, because its behavior is dependent on whether certain vertices of a finite binary tree are leaves (terminal nodes) or not. Similarly for bijections like A127387 and A127379.

Crossrefs

Cf. A153248.

Extensions

Edited by Charles R Greathouse IV, May 13 2010
Showing 1-6 of 6 results.

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