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 1-5 of 5 results.

A154446 Permutation of nonnegative integers: The inverse of A154445.

Original entry on oeis.org

0, 1, 3, 2, 6, 7, 4, 5, 12, 13, 14, 15, 9, 8, 10, 11, 24, 25, 26, 27, 28, 29, 30, 31, 18, 19, 16, 17, 20, 21, 22, 23, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 36, 37, 38, 39, 33, 32, 34, 35, 40, 41, 42, 43, 44, 45, 46, 47, 96, 97, 98, 99, 100, 101, 102
Offset: 0

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Author

Antti Karttunen, Jan 17 2009

Keywords

Links

Crossrefs

Inverse: A154445. a(n) = A153142(A154440(n)) = A054429(A154442(A054429(n))). Cf. A072376, A153141-A153142, A154435-A154436, A154439-A154448. Corresponds to A154456 in the group of Catalan bijections.

Extensions

Spelling/notation corrections by Charles R Greathouse IV, Mar 18 2010

A154450 Signature permutation of a Catalan bijection: The inverse of A154449.

Original entry on oeis.org

0, 1, 2, 3, 5, 4, 6, 7, 8, 12, 13, 11, 9, 10, 15, 14, 16, 17, 18, 19, 20, 21, 22, 31, 32, 34, 35, 36, 30, 33, 28, 24, 23, 29, 25, 26, 27, 40, 41, 39, 37, 38, 43, 42, 44, 45, 46, 47, 48, 49, 50, 52, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 87, 88, 90, 91, 92, 96, 97
Offset: 0

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Author

Antti Karttunen, Jan 17 2009

Keywords

Comments

This automorphism of rooted plane binary trees switches the two descendant trees for every other vertex as it descends along the 111... ray, but not starting swapping until at the right-hand side child of the root, leaving the root itself fixed. Specifically, *A154450 = psi(A154440), where the isomorphism psi is given in A153141 (see further comments there).

Links

Crossrefs

Inverse: A154449. a(n) = A069767(A154456(n)) = A057163(A154454(A057163(n))). Cf. A069770, A154452.
Differs from A089850 for the first time at n=31, where a(31)=24, while A089850(31)=23.

A154452 Signature permutation of a Catalan bijection: The inverse of A154451.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jan 17 2009

Keywords

Comments

This automorphism of rooted plane binary trees switches the two descendant trees for every other vertex as it descends along the 111... ray, starting swapping already at the root. Specifically, *A154452 = psi(A154442), where the isomorphism psi is given in A153141 (see further comments there).

Links

Crossrefs

Inverse: A154451. a(n) = A069767(A154454(n)) = A057163(A154456(A057163(n))). Cf. A069770, A154450.

A154454 Signature permutation of a Catalan bijection: The inverse of A154453.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jan 17 2009

Keywords

Comments

This automorphism of rooted plane binary trees switches the two descendant trees for every other vertex as it descends along the 000... ray, but not starting swapping until at the left-hand side child of the root, leaving the root itself fixed. Specifically, *A154454 = psi(A154444), where the isomorphism psi is given in A153141 (see further comments there).

Links

Crossrefs

Inverse: A154453. a(n) = A069768(A154452(n)) = A057163(A154450(A057163(n))). Cf. A069770, A154456.
Differs from its inverse A154453 for the first time at n=49, where a(49)=64, while A154454(49)=63. Differs from A089854 for the first time at n=49, where a(49)=64, while A089854(49)=63. Differs from A131173 for the first time at n=26, where a(26)=26, while A131173(26)=27.

A154455 Signature permutation of a Catalan bijection induced by generator "b" of the leftward recursing instance of Basilica group wreath recursion: a = (b,1), b = s(a,1).

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jan 17 2009

Keywords

Comments

This automorphism of rooted plane binary trees switches the two descendant trees for every other vertex as it returns back toward the root, after descending down to the leftmost tip of the tree along the 000... ray, so that the last vertex whose descendants are swapped is the root node of the tree. Specifically, *A154455 = psi(A154445), where the isomorphism psi is given in A153141 (see further comments there).

Links

Crossrefs

Inverse: A154456. a(n) = A154449(A069767(n)) = A057163(A154451(A057163(n))). Cf. A069770, A154453.
Differs from A082345 for the first time at n=49, where a(49)=26, while A082345(49)=27. Differs from A122327 for the first time at n=26, where a(26)=49, while A122327(26)=50. Differs from A129612 for the first time at n=195, where a(195)=92, while A129612(195)=91.
Showing 1-5 of 5 results.

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