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 1-9 of 9 results.

A130370 Signature permutation of a Catalan automorphism: inverse of *A130369.

Original entry on oeis.org

0, 1, 3, 2, 7, 8, 4, 5, 6, 17, 18, 20, 21, 22, 10, 9, 11, 12, 13, 14, 15, 16, 19, 45, 46, 48, 49, 50, 54, 55, 57, 58, 59, 61, 62, 63, 64, 26, 27, 23, 24, 25, 29, 28, 30, 31, 32, 33, 34, 35, 36, 38, 37, 39, 40, 41, 42, 43, 44, 47, 51, 52, 53, 56, 60, 129, 130, 132, 133, 134
Offset: 0

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Author

Antti Karttunen, Jun 05 2007

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Inverse: A130369. a(n) = A130371(A074686(n)) = A074686(A130375(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 A130377, LEFT(A019590), A130378 and A130379.

A130377 Number of cycles in range [A014137(n-1)..A014138(n-1)] of permutation A130369/A130370.

Original entry on oeis.org

1, 1, 1, 1, 2, 2, 3, 5, 10, 8, 16, 18, 22, 26
Offset: 0

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Author

Antti Karttunen, Jun 05 2007

Keywords

A130378 Maximum cycle size in range [A014137(n-1)..A014138(n-1)] of permutation A130369/A130370.

Original entry on oeis.org

1, 1, 2, 5, 8, 35, 103, 334, 425, 3401, 6849, 27732, 118268, 325212
Offset: 0

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Author

Antti Karttunen, Jun 05 2007

Keywords

Crossrefs

Cf. A127279.

A130379 Least common multiple of all cycle sizes in range [A014137(n-1)..A014138(n-1)] of permutation A130369/A130370.

Original entry on oeis.org

1, 1, 2, 5, 24, 35, 17304, 105210, 15002667388800, 2803962610087320, 390995845903819693817280, 4427769139935736194600, 426341479886584667397117049422960
Offset: 0

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Author

Antti Karttunen, Jun 05 2007

Keywords

Comments

Note the non-monotone drop from a(10) to a(11).

A130371 Signature permutation of a Catalan automorphism: apply *A074685 to the last subtree, if the root degree (A057515(n)) is odd.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 8, 7, 9, 10, 11, 12, 13, 14, 15, 16, 20, 21, 19, 22, 18, 17, 23, 24, 25, 27, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 55, 54, 47, 57, 58, 59, 51, 52, 53, 61, 62, 56, 63, 48, 49, 60, 64, 50, 46, 45, 65, 66, 67, 68, 69, 70, 71
Offset: 0

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Author

Antti Karttunen, Jun 05 2007

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Crossrefs

Inverse: A130372. a(n) = A130370(A074685(n)) = A074686(A130375(A074685(n))) = A130370(A130375(A130369(n))).

A130372 Signature permutation of a Catalan automorphism: apply *A074686 to the last subtree, if the root degree (A057515(n)) is odd.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 8, 7, 9, 10, 11, 12, 13, 14, 15, 16, 22, 21, 19, 17, 18, 20, 23, 24, 25, 27, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 64, 63, 47, 58, 59, 62, 51, 52, 53, 46, 45, 56, 48, 49, 50, 60, 54, 55, 57, 61, 65, 66, 67, 68, 69, 70, 71
Offset: 0

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Author

Antti Karttunen, Jun 05 2007

Keywords

Links

Crossrefs

Inverse: A130371. a(n) = A074686(A130369(n)) = A074686(A130376(A074685(n))) = A130370(A130376(A130369(n))).

A130375 Signature permutation of a Catalan automorphism: apply *A074685 after the first nil on the top-level of list, if any present, otherwise leave the structure intact.

Original entry on oeis.org

0, 1, 2, 3, 5, 4, 6, 7, 8, 11, 12, 13, 10, 9, 14, 15, 16, 17, 18, 19, 20, 21, 22, 29, 28, 30, 31, 32, 33, 34, 35, 25, 26, 36, 27, 24, 23, 38, 37, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 81, 82, 83, 80, 79, 85, 84
Offset: 0

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Author

Antti Karttunen, Jun 05 2007

Keywords

Links

Crossrefs

Inverse: A130376. a(n) = A074685(A130370(n)) = A074685(A130371(A074686(n))) = A130369(A130371(A130370(n))).

A130376 Signature permutation of a Catalan automorphism: apply *A074686 after the first nil on the top-level of list, if any present, otherwise leave the structure intact.

Original entry on oeis.org

0, 1, 2, 3, 5, 4, 6, 7, 8, 13, 12, 9, 10, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 36, 35, 31, 32, 34, 24, 23, 25, 26, 27, 28, 29, 30, 33, 38, 37, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 106, 105, 100, 101, 104
Offset: 0

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Author

Antti Karttunen, Jun 05 2007

Keywords

Links

Crossrefs

Inverse: A130375. a(n) = A130369(A074686(n)) = A074685(A130372(A074686(n))) = A130369(A130372(A130370(n))).

A130374 Signature permutation of a Catalan automorphism: flip the positions of even- and odd-indexed elements at the top level of the list, leaving the last element in place if the length (A057515(n)) is odd.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 5, 7, 8, 9, 10, 14, 16, 19, 11, 15, 12, 17, 18, 13, 20, 21, 22, 23, 25, 24, 26, 27, 37, 38, 42, 44, 47, 51, 53, 56, 60, 28, 29, 39, 43, 52, 30, 40, 31, 45, 46, 32, 48, 49, 50, 33, 41, 34, 54, 55, 35, 57, 58, 59, 36, 61, 62, 63, 64, 65, 66, 70, 72, 75, 67, 71
Offset: 0

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Author

Antti Karttunen, Jun 05 2007

Keywords

Comments

This self-inverse automorphism permutes the top level of a list of even length (1 2 3 4 ... 2n-1 2n) as (2 1 4 3 ... 2n 2n-1), and when applied to a list of odd length (1 2 3 4 ... 2n-1 2n 2n+1), permutes it as (2 1 4 3 ... 2n 2n-1 2n+1).

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Cf. a(n) = A057508(A130373(A057508(n))) = A057164(A130373(A057164(n))) = A127285(A127288(n)) = A127287(A127286(n)). Also a(A085223(n)) = A130370(A122282(A130369(A085223(n)))) holds for all n>=0. The number of cycles and the number of fixed points in range [A014137(n-1)..A014138(n-1)] of this permutation are given by A073193 and A073192.
Showing 1-9 of 9 results.

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