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 1-8 of 8 results.

A089417 Number of cycles in range [A014137(n-1)..A014138(n-1)] of permutation A082333/A082334.

Original entry on oeis.org

1, 1, 1, 2, 7, 6, 10, 20, 37, 70, 130, 272, 480, 954, 1750, 3462, 6481, 12922, 24372, 48702, 92490
Offset: 0

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Author

Antti Karttunen, Nov 29 2003, Proposed by Wouter Meeussen, Spring 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.
Is the non-monotone notch from a(4)=7 to a(5)=6 the only one?

Links

Crossrefs

Cf. A089411.

A089418 Number of fixed points in range [A014137(n-1)..A014138(n-1)] of permutation A082333/A082334.

Original entry on oeis.org

1, 1, 0, 1, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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

A089419 Maximum cycle size in range [A014137(n-1)..A014138(n-1)] of permutation A082333/A082334.

Original entry on oeis.org

1, 1, 2, 4, 4, 13, 34, 84, 116, 382, 1384, 1984, 2498, 7102, 11944, 22276, 65242, 105118, 186574, 414001, 888856
Offset: 0

Views

Author

Antti Karttunen, Nov 29 2003

Keywords

Links

A089420 Least common multiple of all cycle sizes in range [A014137(n-1)..A014138(n-1)] of permutation A082333/A082334.

Original entry on oeis.org

1, 1, 2, 4, 4, 1716, 79560, 214741800, 19672368075360
Offset: 0

Views

Author

Antti Karttunen, Nov 29 2003

Keywords

Links

A082333 Permutation of natural numbers induced by the composition of involutions A057163 & A082313.

Original entry on oeis.org

0, 1, 3, 2, 8, 4, 6, 5, 7, 22, 10, 19, 12, 17, 20, 9, 15, 13, 18, 14, 11, 21, 16, 64, 27, 60, 32, 46, 61, 25, 52, 35, 49, 51, 30, 58, 44, 62, 26, 53, 31, 45, 55, 24, 41, 36, 50, 39, 33, 59, 47, 54, 23, 40, 34, 48, 38, 29, 63, 56, 37, 28, 57, 43, 42, 196, 78, 191, 92, 134
Offset: 0

Views

Author

Antti Karttunen, Apr 17 2003, Proposed by Wouter Meeussen

Keywords

Links

Crossrefs

Cf. A057163, A082313.
Inverse of A082334. Occurs in A073200 as row 730750818666116073099889616808727458479087976635. Cf. also A082331-A082332.

Formula

a(n) = A057163(A082313(n)).

A082313 Involution of natural numbers: A057501-conjugate of A057164.

Original entry on oeis.org

0, 1, 2, 3, 4, 8, 6, 7, 5, 9, 21, 14, 18, 13, 11, 22, 16, 17, 12, 19, 20, 10, 15, 23, 58, 37, 49, 35, 28, 62, 42, 46, 32, 51, 55, 27, 41, 25, 59, 39, 50, 36, 30, 63, 44, 45, 31, 53, 54, 26, 40, 33, 64, 47, 48, 34, 56, 57, 24, 38, 60, 61, 29, 43, 52, 65, 170, 107, 142, 100
Offset: 0

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Author

Antti Karttunen, Apr 17 2003. Proposed by Wouter Meeussen in Dec 15 2001

Keywords

Comments

Note: This is isomorphic with Meeussen's "skewcatacycleft" operation acting on the interpretation (gg) of the exercise 19 by Stanley.

Links

Crossrefs

a(n) = A069888(A057502(n)). Occurs in A073200 as row 604463486276865131809167. Cf. also A082314, A082315, A082333, A082334.
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) = A057501(A057164(A057502(n)))

A082332 Permutation of natural numbers induced by the composition of involutions A069888 & A057163. &F A082332 a(n) = A069888(A057163(n)).

Original entry on oeis.org

0, 1, 2, 3, 6, 4, 8, 5, 7, 19, 16, 11, 14, 9, 22, 21, 13, 15, 10, 18, 20, 12, 17, 60, 56, 47, 53, 44, 33, 30, 39, 51, 42, 25, 28, 37, 23, 64, 63, 59, 62, 58, 36, 35, 41, 52, 43, 27, 29, 38, 24, 50, 49, 55, 61, 57, 32, 34, 40, 26, 46, 48, 54, 31, 45, 191, 186, 172, 182, 168
Offset: 0

Views

Author

Antti Karttunen, Apr 17 2003

Keywords

Links

Crossrefs

Inverse of A082331. Occurs in A073200 as row 576469548397005071. Cf. also A082333-A082334.

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.
Showing 1-8 of 8 results.

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