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 1-7 of 7 results.

A085159 Permutation of natural numbers induced by the Catalan bijection gma085159 acting on symbolless S-expressions encoded by A014486/A063171.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 7, 5, 8, 9, 11, 14, 16, 19, 17, 20, 12, 10, 13, 21, 15, 18, 22, 23, 25, 28, 30, 33, 37, 39, 42, 44, 47, 51, 53, 56, 60, 45, 48, 54, 57, 61, 31, 34, 26, 24, 27, 35, 29, 32, 36, 58, 62, 40, 38, 41, 49, 43, 46, 50, 63, 52, 55, 59, 64, 65, 67, 70, 72, 75
Offset: 0

Views

Author

Antti Karttunen, Jun 23 2003

Keywords

Comments

This Catalan bijection rotates the interpretations (pp)-(rr) of Stanley, using the "rising slope" mapping illustrated in A085161.

Links

Crossrefs

Inverse: A085160. a(n) = A085161(A085160(A085161(n))) = A085169(A082315(A085170(n))) = A074684(A082315(A074683(n))) = A085173(A085173(n)). Occurs in A073200. Cf. also A085165-A085168, A086429. Scheme-function app-to-xrt given in A085203.
Number of cycles: A054357. Number of fixed points: A046698. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).

A086430 Permutation of natural numbers induced by the Catalan bijection gma086430 acting on symbolless S-expressions encoded by A014486/A063171.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 7, 5, 8, 9, 11, 14, 16, 19, 17, 18, 12, 10, 15, 20, 21, 13, 22, 23, 25, 28, 30, 33, 37, 39, 42, 44, 47, 51, 53, 56, 60, 45, 46, 48, 49, 50, 31, 32, 26, 24, 29, 40, 38, 43, 52, 54, 55, 57, 58, 59, 34, 35, 27, 41, 61, 62, 63, 36, 64, 65, 67, 70, 72, 75
Offset: 0

Views

Author

Antti Karttunen, Jun 23 2003

Keywords

Comments

This Catalan bijection rotates the interpretations (pp)-(rr) of Stanley, using the "descending slope" mapping illustrated in A086431.

Links

Crossrefs

Inverse: A086429. a(n) = A086428(A086428(n)) = A086431(A086429(A086431(n))) = A057164(A085160(A057164(n))) = A086425(A082316(A086426(n))). Occurs in A073200.
Number of cycles: A054357. Number of fixed points: A046698. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).

A086425 Permutation of natural numbers induced by the Catalan bijection gma086425 acting on symbolless S-expressions encoded by A014486/A063171.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jun 23 2003

Keywords

Links

Crossrefs

Inverse: A086426. a(n) = A057164(A074684(n)). Occurs in A073200. Cf. also A086427, A086428, A086429, A086430, A086431.

A086426 Permutation of natural numbers induced by the Catalan bijection gma086426 acting on symbolless S-expressions encoded by A014486/A063171.

Original entry on oeis.org

0, 1, 3, 2, 7, 8, 6, 5, 4, 17, 20, 18, 22, 21, 16, 19, 15, 12, 13, 14, 11, 10, 9, 45, 54, 48, 61, 57, 46, 55, 50, 63, 64, 49, 62, 59, 58, 44, 53, 47, 60, 56, 43, 52, 40, 31, 34, 41, 32, 36, 35, 42, 51, 39, 30, 33, 38, 29, 26, 27, 37, 28, 25, 24, 23, 129, 157, 138, 180, 166
Offset: 0

Views

Author

Antti Karttunen, Jun 23 2003

Keywords

Links

Crossrefs

Inverse: A086425. a(n) = A074683(A057164(n)). Occurs in A073200. Cf. also A086427, A086428, A086429, A086430, A086431.

A086427 Permutation of natural numbers induced by the Catalan bijection gma086427 acting on symbolless S-expressions encoded by A014486/A063171.

Original entry on oeis.org

0, 1, 3, 2, 8, 6, 7, 5, 4, 22, 19, 20, 15, 14, 21, 16, 18, 13, 12, 17, 10, 11, 9, 64, 60, 61, 52, 51, 62, 53, 55, 41, 40, 54, 38, 39, 37, 63, 56, 57, 43, 42, 59, 47, 50, 36, 34, 49, 35, 32, 31, 58, 44, 46, 27, 26, 48, 29, 33, 30, 45, 24, 25, 28, 23, 196, 191, 192, 178, 177
Offset: 0

Views

Author

Antti Karttunen, Jun 23 2003

Keywords

Comments

This Catalan bijection rotates by "half step" the interpretations (pp)-(rr) of Stanley, using the "descending slope" mapping illustrated in A086431.

Links

Crossrefs

Inverse: A086428. a(n) = A086431(A086428(A086431(n))) = A057164(A085173(A057164(n))) = A086425(A057501(A086426(n))). Occurs in A073200. Cf. also A086429 (whole step rotate).
Number of cycles: A002995. Number of fixed points: A019590. Max. cycle size: A057543. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).

A085165 A057163-conjugate of A085159.

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 5, 6, 8, 9, 12, 16, 17, 21, 10, 18, 11, 14, 15, 13, 19, 20, 22, 23, 26, 30, 31, 35, 42, 43, 44, 45, 49, 56, 57, 58, 63, 24, 32, 47, 46, 59, 25, 48, 28, 37, 38, 29, 39, 40, 41, 27, 50, 33, 51, 52, 34, 53, 54, 55, 36, 60, 61, 62, 64, 65, 68, 72, 73, 77
Offset: 0

Views

Author

Antti Karttunen, Jun 23 2003

Keywords

Links

Crossrefs

Inverse: A085166. a(n) = A057163(A085159(A057163(n))) = A085162(A085166(A085162(n))). Occurs in A073200. Cf. also A085162, A086429, A086430.
Number of cycles: A054357. Number of fixed points: A046698. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).

A085166 A057163-conjugate of A085160.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jun 23 2003

Keywords

Links

Crossrefs

Inverse: A085165. a(n) = A057163(A085160(A057163(n))) = A085162(A085165(A085162(n))). Occurs in A073200. Cf. also A085162, A086429, A086430.
Number of cycles: A054357. Number of fixed points: A046698. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).
Showing 1-7 of 7 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.