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 1-10 of 11 results. Next

A089875 Least common multiple of all cycle sizes in range [A014137(n-1)..A014138(n-1)] of permutation A071665/A071666.

Original entry on oeis.org

1, 1, 1, 3, 3, 15, 30, 180, 3780, 291060, 3783780, 70982929216999800
Offset: 0

Views

Author

Antti Karttunen, Nov 29 2003

Keywords

Links

Crossrefs

Cf. A089403.

A089872 Number of cycles in range [A014137(n-1)..A014138(n-1)] of permutation A071665/A071666.

Original entry on oeis.org

1, 1, 2, 3, 6, 16, 40, 93, 226, 540, 1336, 3284, 8068, 19664, 47880, 116407, 282866, 687666, 1673920, 4077020, 9929636
Offset: 0

Views

Author

Antti Karttunen, Nov 29 2003

Keywords

Comments

The number of orbits to which the corresponding automorphism(s) partitions the set of A000108(n) binary trees with n internal nodes.

Links

A089873 Number of fixed points in range [A014137(n-1)..A014138(n-1)] of permutation A071665/A071666.

Original entry on oeis.org

1, 1, 2, 2, 2, 4, 4, 4, 10, 6, 10, 12, 16, 20, 36, 28, 56, 46, 104, 84, 166
Offset: 0

Views

Author

Antti Karttunen, Nov 29 2003

Keywords

Comments

The number of n-node binary trees fixed by the corresponding automorphism(s).

Links

A089874 Maximum cycle size in range [A014137(n-1)..A014138(n-1)] of permutation A071665/A071666.

Original entry on oeis.org

1, 1, 1, 3, 3, 5, 6, 18, 45, 147, 147, 267, 801, 2538, 3255, 7665, 29484, 67644, 164088, 515592, 1657785
Offset: 0

Views

Author

Antti Karttunen, Nov 29 2003

Keywords

Links

A057506 Signature-permutation of a Catalan Automorphism: (inverse of) "Donaghey's map M", acting on the parenthesizations encoded by A014486.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Sep 03 2000

Keywords

Comments

This is inverse of A057505, which is a signature permutation of Catalan automorphism (bijection) known as "Donaghey's map M". See A057505 for more comments, links and references.

Links

Crossrefs

Inverse: A057505.
Cf. A057161, A057162, A057163, A057164, A057501, A057502, A057503, A057504 (for similar signature permutations of simple Catalan automorphisms).
Cf. A057507 (cycle counts).
The 2nd, 3rd, 4th, 5th and 6th "powers" of this permutation: A071662, A071664, A071666, A071668, A071670.
Row 12 of table A122287.
Cf. also A014486, A080300, A080069, A080070.

Programs

  • Maple
    map(CatalanRankGlobal,map(DonagheysA057506,CatalanSequences(196))); # Where CatalanSequences(n) gives the terms A014486(0..n).
DonagheysA057506 := n -> pars2binexp(deepreverse(DonagheysA057505(deepreverse(binexp2pars(n)))));
DonagheysA057505 := h -> `if`((0 = nops(h)), h, [op(DonagheysA057505(car(h))), DonagheysA057505(cdr(h))]);
# The following corresponds to automorphism A057164:
deepreverse := proc(a) if 0 = nops(a) or list <> whattype(a) then (a) else [op(deepreverse(cdr(a))), deepreverse(a[1])]; fi; end;
# The rest of required Maple-functions: see the given OEIS Wiki page.
  • Scheme
    (define (A057506 n) (CatalanRankSexp (*A057506 (CatalanUnrankSexp n))))
(define (*A057506 bt) (let loop ((lt bt) (nt (list))) (cond ((not (pair? lt)) nt) (else (loop (cdr lt) (cons nt (*A057506 (car lt))))))))
;; Functions CatalanRankSexp and CatalanUnrankSexp can be found at OEIS Wiki page.

Formula

a(n) = A057163(A057164(n)).
a(n) = A057163(A057505(A057163(n))) = A057164(A057505(A057164(n))).

Extensions

Entry revised by Antti Karttunen, May 30 2017

A071662 Permutation A057506 applied twice ("squared").

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 5, 6, 8, 9, 17, 12, 16, 21, 10, 18, 11, 14, 20, 13, 15, 19, 22, 23, 45, 31, 44, 58, 26, 49, 30, 42, 57, 35, 43, 56, 63, 24, 46, 32, 47, 59, 25, 48, 28, 37, 54, 34, 40, 53, 62, 27, 50, 29, 38, 55, 33, 39, 51, 61, 36, 41, 52, 60, 64, 65, 129, 87, 128, 170, 73
Offset: 0

Views

Author

Antti Karttunen, May 30 2002

Keywords

Links

Crossrefs

Inverse permutation: A071661 and also its car/cdr-flipped conjugate, i.e. A071662(n) = A057163(A071661(A057163(n))) = A057506(A057506(n)). Cf. also A071664, A071666, A071668, A071670.

A071665 Permutation A057505 applied four times ("^4"), permutation A071661 squared.

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 5, 6, 8, 9, 17, 12, 16, 21, 10, 18, 11, 14, 20, 13, 15, 19, 22, 23, 45, 31, 44, 58, 26, 49, 30, 42, 57, 35, 40, 56, 63, 24, 46, 32, 43, 59, 25, 47, 28, 37, 54, 48, 34, 53, 62, 27, 50, 29, 38, 55, 33, 39, 51, 61, 36, 41, 52, 60, 64, 65, 129, 87, 128, 170, 73
Offset: 0

Views

Author

Antti Karttunen, May 30 2002

Keywords

Links

Crossrefs

Inverse permutation: A071666 and also its car/cdr-flipped conjugate, i.e. A071665(n) = A057163(A071666(A057163(n))) = A057505(A071663(n)) = A071661(A071661(n)). Cf. also A071667, A071669.

A071668 Permutation A057506 applied five times ("^5").

Original entry on oeis.org

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

Views

Author

Antti Karttunen, May 30 2002

Keywords

Links

Crossrefs

Inverse permutation: A071667 and also its car/cdr-flipped conjugate, i.e. A071668(n) = A057163(A071667(A057163(n))) = A057506(A071666(n)). Cf. also A071662, A071664, A071670.

A071664 Permutation A057506 applied three times ("cubed").

Original entry on oeis.org

0, 1, 3, 2, 8, 5, 6, 7, 4, 22, 13, 15, 18, 10, 19, 11, 20, 21, 12, 14, 16, 17, 9, 64, 36, 41, 50, 27, 52, 29, 55, 59, 32, 38, 47, 46, 24, 60, 33, 39, 48, 25, 61, 34, 62, 63, 35, 40, 43, 49, 26, 51, 28, 53, 56, 30, 54, 57, 58, 31, 37, 42, 44, 45, 23, 196, 106, 120, 148, 78
Offset: 0

Views

Author

Antti Karttunen, May 30 2002

Keywords

Links

Crossrefs

Inverse permutation: A071663 and also its car/cdr-flipped conjugate, i.e. A071664(n) = A057163(A071663(A057163(n))) = A057506(A071662(n)). Cf. also A071666, A071668, A071670.

A125977 Signature-permutation of a Catalan automorphism: composition of A057163 and A125976.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 7, 5, 8, 9, 14, 16, 11, 19, 17, 20, 12, 10, 15, 21, 18, 13, 22, 23, 37, 42, 28, 51, 44, 53, 30, 25, 39, 56, 47, 33, 60, 45, 54, 57, 48, 61, 31, 40, 26, 24, 38, 43, 34, 29, 52, 58, 62, 49, 46, 55, 35, 32, 27, 41, 63, 59, 50, 36, 64, 65, 107, 121, 79, 149
Offset: 0

Views

Author

Antti Karttunen, Jan 02 2007

Keywords

Links

Crossrefs

Inverse: A125978. a(n) = A057163(A125976(n)). The number of cycles, maximum cycle sizes and LCM's of all cycle sizes in range [A014137(n-1)..A014138(n-1)] of this permutation are given by A126317, A126318 and A126319. The number of fixed points seems to be given by A123050 and fixed points themselves are probably given by A126312. Cf. also A126313-A126316.
Differs from A071661 for the first time at n=43, where a(n)=40, while A071661(43)=34. Differs from A071666 for the first time at n=34, where a(n)=47, while A071666(34)=48.
Showing 1-10 of 11 results. Next

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

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