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 10 results.

A089877 Number of fixed points in range [A014137(n-1)..A014138(n-1)] of permutation A071667/A071668.

Original entry on oeis.org

1, 1, 0, 0, 0, 5, 0, 0, 0, 5, 0, 10, 0, 5, 0, 10, 0, 45, 0, 10, 0
Offset: 0

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Author

Antti Karttunen, Nov 29 2003

Keywords

Comments

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

Links

A089876 Number of cycles in range [A014137(n-1)..A014138(n-1)] of permutation A071667/A071668.

Original entry on oeis.org

1, 1, 1, 2, 3, 14, 22, 62, 127, 320, 756, 1888, 4440, 10996, 26784, 67004, 166449, 417848, 1041262, 2596506, 6427116
Offset: 0

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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

A089878 Maximum cycle size in range [A014137(n-1)..A014138(n-1)] of permutation A071667/A071668.

Original entry on oeis.org

1, 1, 2, 3, 6, 6, 24, 72, 144, 147, 588, 672, 2136, 10152, 11496, 29484, 117936, 270576, 656352, 2062368, 3184728
Offset: 0

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Author

Antti Karttunen, Nov 29 2003

Keywords

Links

Crossrefs

For the terms a(0)-a(20) differs from A057545 only at n=14 where a(14)=11496 != A057545(14)=11520 and at n=20, where a(20)=3184728 while A057545(20)=4040160.

A089879 Least common multiple of all cycle sizes in range [A014137(n-1)..A014138(n-1)] of permutation A071667/A071668.

Original entry on oeis.org

1, 1, 2, 6, 6, 6, 24, 144, 3024, 232848, 3027024, 56786343373599840
Offset: 0

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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

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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

A071666 Permutation A057506 applied four times ("^4"), permutation A071662 squared.

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, 48, 33, 60, 45, 54, 57, 34, 61, 31, 40, 26, 24, 38, 43, 47, 29, 52, 58, 62, 49, 46, 55, 35, 32, 27, 41, 63, 59, 50, 36, 64, 65, 107, 121, 79, 149, 126
Offset: 0

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Author

Antti Karttunen, May 30 2002

Keywords

Links

Crossrefs

Inverse permutation: A071665 and also its car/cdr-flipped conjugate, i.e. A071666(n) = A057163(A071665(A057163(n))) = A057506(A071664(n)) = A071662(A071662(n)). Cf. also A071662, A071668, A071670.

A071667 Permutation A057505 applied five times ("^5").

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, 34, 38, 37, 63, 56, 57, 40, 42, 59, 43, 50, 36, 33, 47, 48, 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, May 30 2002

Keywords

Links

Crossrefs

Inverse permutation: A071668 and also its car/cdr-flipped conjugate, i.e. A071667(n) = A057163(A071668(A057163(n))) = A057505(A071665(n)). Cf. also A071661, A071663, A071669.

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.

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.

A071670 Permutation A057506 applied six times ("^6"), permutation A071662 cubed, permutation A071664 squared.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, May 30 2002

Keywords

Links

Crossrefs

Inverse permutation: A071669 and also its car/cdr-flipped conjugate, i.e. A071670(n) = A057163(A071669(A057163(n))) = A057506(A071668(n)) = A071662(A071662(A071662(n))) = A071664(A071664(n)). Cf. also A071666.
Showing 1-10 of 10 results.

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