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.

A127282 Number of fixed points in range [A014137(n-1)..A014138(n-1)] of permutation A126315/A126316.

Original entry on oeis.org

1, 1, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0
Offset: 0

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Author

Antti Karttunen, Jan 16 2007

Keywords

Crossrefs

A127278.

A127283 Maximum cycle size in range [A014137(n-1)..A014138(n-1)] of permutation A126315/A126316.

Original entry on oeis.org

1, 1, 2, 3, 4, 14, 18, 38, 158, 190, 618, 1274, 17094
Offset: 0

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Author

Antti Karttunen, Jan 16 2007

Keywords

Crossrefs

A127279.

A127281 Number of cycles in range [A014137(n-1)..A014138(n-1)] of permutation A126315/A126316.

Original entry on oeis.org

1, 1, 1, 2, 5, 8, 20, 30, 69, 116, 278, 416, 898
Offset: 0

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Author

Antti Karttunen, Jan 16 2007

Keywords

A126313 Signature-permutation of a Catalan automorphism: composition of A069772 and A125976.

Original entry on oeis.org

0, 1, 3, 2, 8, 5, 6, 4, 7, 22, 13, 15, 12, 14, 19, 21, 16, 11, 18, 10, 20, 17, 9, 64, 36, 41, 35, 40, 52, 53, 38, 34, 39, 55, 51, 37, 54, 60, 63, 32, 62, 31, 56, 59, 47, 33, 50, 27, 58, 49, 26, 43, 44, 29, 61, 30, 24, 57, 48, 25, 46, 42, 28, 23, 45, 196, 106, 120, 105, 119
Offset: 0

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Author

Antti Karttunen, Jan 16 2007

Keywords

Comments

Like A069771, A069772, A125976 and A126315/A126316, this automorphism keeps symmetric Dyck paths symmetric, but not necessarily same.

Links

Crossrefs

Inverse: A126314. a(n) = A069772(A125976(n)) = A126290(A069772(n)) = A126315(A057164(n)). The number of cycles, number of fixed points, maximum cycle sizes and LCM's of all cycle sizes in range [A014137(n-1)..A014138(n-1)] of this permutation are given by A127277, A127278, A127279 and A127280. The fixed points are given by A127306. Note the curiosity: this automorphism partitions the A000108(8) = 1430 Catalan structures of size eight (e.g. Dyck paths of length 16) into 79 equivalence classes, of which the largest contains 79 members.

A125977 Signature-permutation of a Catalan automorphism: composition of A057163 and A125976.

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

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Author

Antti Karttunen, Jan 02 2007

Keywords

Links

Crossrefs

Inverse: A125978. a(n) = A057163(A125976(n)). The number of cycles, maximum cycle sizes and LCM's of all cycle sizes in range [A014137(n-1)..A014138(n-1)] of this permutation are given by A126317, A126318 and A126319. The number of fixed points seems to be given by A123050 and fixed points themselves are probably given by A126312. Cf. also A126313-A126316.
Differs from A071661 for the first time at n=43, where a(n)=40, while A071661(43)=34. Differs from A071666 for the first time at n=34, where a(n)=47, while A071666(34)=48.

A126314 Signature-permutation of a Catalan automorphism: composition of A125976 and A069772.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jan 16 2007

Keywords

Comments

Like A069771, A069772, A125976 and A126315/A126316, this automorphism keeps symmetric Dyck paths symmetric, but not necessarily same.

Links

Crossrefs

Inverse: A126313. a(n) = A125976(A069772(n)) = A069772(A126290(n)) = A057164(A126316(n)).

A126315 Signature-permutation of a Catalan automorphism: composition of A069771 and A125976.

Original entry on oeis.org

0, 1, 3, 2, 8, 6, 5, 4, 7, 22, 19, 15, 16, 10, 13, 21, 12, 11, 20, 14, 18, 17, 9, 64, 60, 52, 56, 43, 41, 32, 38, 47, 29, 55, 27, 24, 46, 36, 63, 53, 59, 44, 35, 62, 34, 33, 61, 51, 58, 57, 42, 40, 31, 39, 50, 30, 37, 49, 48, 28, 54, 26, 25, 23, 45, 196, 191, 178, 186, 164
Offset: 0

Views

Author

Antti Karttunen, Jan 16 2007

Keywords

Comments

Like A069771, A069772, A125976 and A126313/A126314, this automorphism keeps symmetric Dyck paths symmetric, but not necessarily same.

Links

Crossrefs

Inverse: A126316. a(n) = A069771(A125976(n)) = A126290(A069771(n)) = A126313(A057164(n)). The number of cycles, number of fixed points and maximum cycle sizes in range [A014137(n-1)..A014138(n-1)] of this permutation are given by A127281, A127282 and A127283. See also the comment at A127280.

A127280 Least common multiple of all cycle sizes in range [A014137(n-1)..A014138(n-1)] of permutation A126313/A126314.

Original entry on oeis.org

1, 1, 2, 3, 4, 168, 360, 465585120, 4122326466720, 217481422952137966221600, 423596249162987984485389187200, 2601085547436195054585834389287071368256718712872622796333077962782445499276184000
Offset: 0

Views

Author

Antti Karttunen, Jan 16 2007

Keywords

Comments

The sequence seems to give the least common multiples also for the permutation A126315/A126316, but with a(3)=6 instead of 3.
Showing 1-8 of 8 results.

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