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.

A127278 Number of fixed points in range [A014137(n-1)..A014138(n-1)] of permutation A126313/A126314.

Original entry on oeis.org

1, 1, 0, 2, 4, 2, 0, 4, 0, 1, 0, 0, 0
Offset: 0

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Author

Antti Karttunen, Jan 16 2007

Keywords

Crossrefs

Fixed points themselves are given in A127306. Cf. A127282.

A127279 Maximum cycle size in range [A014137(n-1)..A014138(n-1)] of permutation A126313/A126314.

Original entry on oeis.org

1, 1, 2, 3, 4, 8, 10, 32, 79, 176, 612, 644, 8547
Offset: 0

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Author

Antti Karttunen, Jan 16 2007

Keywords

Crossrefs

A127283.

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.

A127306 Fixed points of permutation A126313/A126314.

Original entry on oeis.org

0, 1, 5, 6, 12, 16, 18, 20, 49, 57, 287, 291, 349, 353, 5791
Offset: 0

Views

Author

Antti Karttunen, Jan 16 2007

Keywords

Comments

Those i, for which A126313(i)=i. Cf. A126312, A127278.

A127277 Number of cycles in range [A014137(n-1)..A014138(n-1)] of permutation A126313/A126314.

Original entry on oeis.org

1, 1, 1, 3, 7, 10, 24, 39, 79, 148, 288, 528, 912
Offset: 0

Views

Author

Antti Karttunen, Jan 16 2007

Keywords

Crossrefs

Cf. A014137, A014138, A126313, A126314.

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

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: 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.

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.

A126316 Signature-permutation of a Catalan automorphism: composition of A125976 and A069771.

Original entry on oeis.org

0, 1, 3, 2, 7, 6, 5, 8, 4, 22, 13, 17, 16, 14, 19, 11, 12, 21, 20, 10, 18, 15, 9, 63, 35, 62, 61, 34, 59, 32, 55, 52, 29, 45, 44, 42, 37, 56, 30, 53, 51, 28, 50, 27, 41, 64, 36, 31, 58, 57, 54, 47, 25, 39, 60, 33, 26, 49, 48, 40, 24, 46, 43, 38, 23, 196, 120, 106, 148, 78
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: A126315. a(n) = A125976(A069771(n)) = A069771(A126290(n)) = A057164(A126314(n)).
Showing 1-8 of 8 results.

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