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.

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A081160 Number of even cycles in range [A014137(n-1)..A014138(n-1)] of permutation A057505/A057506, with two fixed-points of A057164.

Original entry on oeis.org

0, 0, 1, 1, 3, 4, 10, 16, 35, 60, 126, 225, 462, 848, 1716, 3188, 6435, 12095, 24310
Offset: 0

Views

Author

Wouter Meeussen and Antti Karttunen, Mar 10 2003

Keywords

Crossrefs

Bisections: A001700 (shifted right and prepended with zero) and A081161.
Cf. A081150, A081157, A081162.
Cf. A014137, A014138, A057505, A057506, A057164.

A127299 Signature-permutation of A057164-conjugate of Elizalde's and Deutsch's 2003 bijection for Dyck paths.

Original entry on oeis.org

0, 1, 3, 2, 5, 8, 7, 6, 4, 15, 18, 10, 13, 21, 20, 22, 12, 11, 19, 17, 16, 14, 9, 29, 32, 52, 55, 62, 43, 46, 38, 41, 49, 24, 27, 35, 58, 34, 36, 57, 59, 64, 48, 50, 40, 39, 47, 26, 25, 33, 56, 61, 63, 54, 53, 60, 31, 30, 28, 51, 45, 44, 42, 37, 23, 113, 116, 136, 139, 146
Offset: 0

Views

Author

Antti Karttunen, Jan 16 2007

Keywords

References

  • Emeric Deutsch and Sergi Elizalde, A simple and unusual bijection for Dyck paths and its consequences, Annals of Combinatorics, 7 (2003), no. 3, 281-297.

Links

Crossrefs

Inverse: A127300. a(n) = A057164(A127291(A057164(n))) = A057164(A127289(n)).

Programs

A081153 Number of odd cycles in range [A014137(n-1)..A014138(n-1)] of permutation A057505/A057506, with no fixed points of either A057163 or A057164.

Original entry on oeis.org

0, 0, 0, 0, 0, 2, 0, 6, 0, 18, 0, 50, 0, 142, 0, 388, 0, 1114, 0
Offset: 0

Views

Author

Wouter Meeussen and Antti Karttunen Mar 10 2003

Keywords

Crossrefs

Bisection: A081154.
Cf. A081148, A081155.
Cf. A014137, A014138, A057505, A057506, A057163, A057164.

Formula

a(n) = A081148(n)-A081155(n).

A081155 Number of odd cycles in range [A014137(n-1)..A014138(n-1)] of permutation A057505/A057506, with fixed-points of both A057163 and A057164.

Original entry on oeis.org

1, 1, 0, 1, 0, 2, 0, 3, 0, 6, 0, 12, 0, 20, 0, 59, 0, 120, 0
Offset: 0

Views

Author

Wouter Meeussen and Antti Karttunen, Mar 10 2003

Keywords

Comments

See comment at A080973. Because A057163 can fix only binary trees of odd size, the even-indexed terms are all 0 after n>0.

Crossrefs

Bisection: A081156.
Cf. A081148, A081153.
Cf. A014137, A014138, A057505, A057506, A057163, A057164.

Formula

a(n) = A081148(n)-A081153(n).

A081156 Number of odd cycles in range [A014137(2n)..A014138(2n)] of permutation A057505/A057506, with fixed-points of both A057163 and A057164.

Original entry on oeis.org

1, 1, 2, 3, 6, 12, 20, 59, 120
Offset: 0

Views

Author

Wouter Meeussen & Antti Karttunen Mar 10 2003

Keywords

Comments

See comment at A080973.

Crossrefs

Cf. A080973.
Cf. A081155, A000108, A081163.
Cf. A014137, A014138, A057505, A057506, A057163, A057164.

Formula

a(n) = A081155(2n+1) = A000108(n) - 2*A081163(n).

A081158 Number of even cycles in range [A014137(2n-1)..A014138(2n-1)] of permutation A057505/A057506, with no fixed points of A057164.

Original entry on oeis.org

0, 0, 0, 8, 60, 402, 2474, 14496, 84282, 492048
Offset: 0

Views

Author

Wouter Meeussen and Antti Karttunen, Mar 10 2003

Keywords

Crossrefs

Cf. A081157, A081151, A001700.
Cf. A014137, A014138, A057505, A057506, A057164.

Formula

a(n) = A081157(2n) = A081151(n) - A001700(n-1) [where A001700(-1) is taken as 0 here].

A081159 Number of even cycles in range [A014137(2n)..A014138(2n)] of permutation A057505/A057506, with no fixed points of either A057163 or A057164.

Original entry on oeis.org

0, 0, 2, 20, 148, 986, 5918, 34708, 202664
Offset: 0

Views

Author

Wouter Meeussen and Antti Karttunen, Mar 10 2003

Keywords

Crossrefs

Cf. A081157, A014137, A014138, A057505, A057506, A057163, A057164.

Formula

a(n) = A081157(2n+1).

A081161 Number of even cycles in range [A014137(2n)..A014138(2n)] of permutation A057505/A057506, with two fixed-points of A057164.

Original entry on oeis.org

0, 1, 4, 16, 60, 225, 848, 3188, 12095
Offset: 0

Views

Author

Wouter Meeussen and Antti Karttunen, Mar 10 2003

Keywords

Crossrefs

Cf. A081160, A014137, A014138, A057505, A057506, A057164.

Formula

a(n) = A081160(2n+1).

A082314 Involution of natural numbers: A057502-conjugate of A057164.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 8, 7, 6, 9, 11, 10, 12, 13, 21, 22, 20, 17, 18, 19, 16, 14, 15, 23, 28, 25, 30, 33, 24, 29, 26, 31, 34, 27, 32, 35, 36, 58, 62, 59, 63, 64, 57, 61, 54, 45, 48, 55, 46, 49, 50, 56, 60, 53, 44, 47, 51, 42, 37, 39, 52, 43, 38, 40, 41, 65, 79, 70, 84, 93
Offset: 0

Views

Author

Antti Karttunen, Apr 17 2003

Keywords

Links

Crossrefs

a(n) = A057502(A069889(n)). Occurs in A073200 as row 2361759710983228099211. Cf. also A082313.
Number of cycles: A007123. Number of fixed-points: A001405. Max. cycle size: A046698. LCM of cycle sizes: A046698. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).

Formula

a(n) = A057502(A057164(A057501(n)))

A130921 Signature permutation of a Catalan automorphism: composition of automorphisms *A074684 and *A057164.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jun 11 2007

Keywords

Links

Crossrefs

Inverse: A130922. a(n) = A074684(A057164(n)). Cf. A086425.
Previous Showing 11-20 of 78 results. Next

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