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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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).

A081163 Number of even cycles in range [A014137(2n)..A014138(2n)] of permutation A057505/A057506, with two fixed-points of A057163.

Original entry on oeis.org

0, 0, 0, 1, 4, 15, 56, 185, 655
Offset: 0

Views

Author

Wouter Meeussen and Antti Karttunen, Mar 10 2003

Keywords

Crossrefs

Cf. A081162, A000108, A081156.
Cf. A014137, A014138, A057505, A057506, A057163.

Formula

a(n) = A081162(2n+1) = (A000108(n) - A081156(n))/2.

A082331 Permutation of natural numbers induced by the composition of involutions A057163 & A069888.

Original entry on oeis.org

0, 1, 2, 3, 5, 7, 4, 8, 6, 13, 18, 11, 21, 16, 12, 17, 10, 22, 19, 9, 20, 15, 14, 36, 50, 33, 59, 47, 34, 48, 29, 63, 56, 28, 57, 43, 42, 35, 49, 30, 58, 44, 32, 46, 27, 64, 60, 25, 61, 52, 51, 31, 45, 26, 62, 53, 24, 55, 41, 39, 23, 54, 40, 38, 37, 106, 148, 102, 176, 144
Offset: 0

Views

Author

Antti Karttunen, Apr 17 2003, Proposed by Wouter Meeussen

Keywords

Comments

a(n) = A057163(A069888(n))

Links

Crossrefs

Inverse of A082332. Occurs in A073200 as row 9223512774351650875. Cf. also A082333-A082334.

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).

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).

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).

A125980 Signature-permutation of a Catalan automorphism: A057163-conjugate of A125976.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jan 02 2007

Keywords

Comments

This is self-inverse permutation (involution) of the nonnegative integers.

Links

Crossrefs

a(n) = A057163(A125976(A057163(n))) = A125977(A057163(n)) = A057163(A125978(n)).

A125983 Signature-permutation of a Catalan automorphism: A057163-conjugate of A125981.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jan 02 2007

Keywords

Links

Crossrefs

Inverse: A125984. a(n) = A057163(A125981(A057163(n))).

A125984 Signature-permutation of a Catalan automorphism: A057163-conjugate of A125982.

Original entry on oeis.org

0, 1, 3, 2, 7, 8, 5, 6, 4, 18, 17, 20, 21, 22, 12, 13, 15, 16, 19, 10, 11, 14, 9, 49, 50, 46, 48, 45, 55, 54, 57, 59, 58, 61, 62, 63, 64, 32, 31, 34, 35, 36, 40, 41, 43, 47, 44, 52, 53, 56, 60, 26, 27, 29, 30, 33, 38, 39, 42, 51, 24, 25, 28, 37, 23, 143, 142, 146, 147, 148
Offset: 0

Views

Author

Antti Karttunen, Jan 02 2007

Keywords

Links

Crossrefs

Inverse: A125983. a(n) = A057163(A125982(A057163(n))).
Previous Showing 21-30 of 167 results. Next

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