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.

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.

A127387 Signature-permutation of a Catalan automorphism, a self-inverse variant of A127377.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jan 16 2007

Keywords

Comments

Used to construct A127388.

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 A127385 and A127389. (This automorphism has the same fixed points as A127377/A127378). A127302(a(n)) = A127302(n) holds for all n.

A127383 Number of cycles in range [A014137(n-1)..A014138(n-1)] of permutation A127377/A127378.

Original entry on oeis.org

1, 1, 1, 2, 6, 15, 46, 141, 446, 1427, 4722, 15884, 54224, 187380
Offset: 0

Views

Author

Antti Karttunen, Jan 16 2007

Keywords

Crossrefs

A127384, A127385, A127389.

A127385 Number of cycles in range [A014137(n-1)..A014138(n-1)] of permutation A127387.

Original entry on oeis.org

1, 1, 1, 3, 8, 23, 71, 226, 743, 2500, 8570, 29828, 105116, 374308
Offset: 0

Views

Author

Antti Karttunen, Jan 16 2007

Keywords

Crossrefs

A127383, A127386, A127389.

A152173 a(n) is the number of Dyck paths of length n without height of peaks 1 (mod 3) and height of valleys 2 (mod 3).

Original entry on oeis.org

1, 0, 1, 2, 4, 10, 23, 56, 138, 344, 870, 2220, 5716, 14828, 38717, 101682, 268416, 711810, 1895432, 5066030, 13586082, 36547534, 98593064, 266661162, 722953814, 1964358938, 5348367006, 14589803090, 39870312218, 109136843138
Offset: 2

Views

Author

Jun Ma (majun(AT)math.sinica.edu.tw), Nov 27 2008

Keywords

Links

Crossrefs

Cf. A127389. - R. J. Mathar, Dec 03 2008

Programs

  • Mathematica
    CoefficientList[Series[(1-x-Sqrt[1-2x-3x^2+4x^4])/(2x^2 (1+x)),{x,0,30}],x] (* Harvey P. Dale, Feb 10 2015 *)

Formula

G.f.: (1 - x - sqrt(1 - 2*x - 3*x^2 + 4*x^4))/(2(1+x)x^2).
Conjecture: -n*a(n) + (n-3)*a(n-1) + (5*n-12)*a(n-2) + 3*(n-3)*a(n-3) + 4*(6-n)*a(n-4) + 4*(6-n)*a(n-5) = 0. - R. J. Mathar, Aug 14 2012
G.f.: 1/x^2 - 2/x + 2/(1+x) + G(0)/x where G(k) = 1 - 1/(x + x^2/(1 + x/G(k+1))); (continued fraction, 3-step). - Sergei N. Gladkovskii, Nov 28 2012
Showing 1-5 of 5 results.

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

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