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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A127382 Signature-permutation of the inverse of Callan's 2006 bijection (A127381) on Dyck Paths.

Original entry on oeis.org

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

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Antti Karttunen, Jan 16 2007

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Inverse: A127381. a(n) = A057164(A127380(A057164(n))).

A127384 Number of cycles in range [A014137(n-1)..A014138(n-1)] of permutations A127379/A127380 and A127381/A127382.

Original entry on oeis.org

1, 1, 2, 4, 9, 23, 62, 179, 543, 1705, 5482, 18056, 60634, 206824
Offset: 0

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Antti Karttunen, Jan 16 2007

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A127383.

A127379 Signature-permutation of Callan's 2006 bijection on Dyck Paths, mirrored version (A057164-conjugate).

Original entry on oeis.org

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

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Author

Antti Karttunen, Jan 16 2007

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It's much easier to implement Callan's 2006 bijection for S-expressions if one considers a mirror-image of the graphical description given by Callan (on page 3). Then this automorphism is just RIBS-transformation (explained in A122200) of the automorphism A127377 and Callan's original variant A127381 is obtained as A057164(a(A057164(n))).

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Inverse: A127380. a(n) = A057164(A127381(A057164(n))). The number of cycles and the number of fixed points in range [A014137(n-1)..A014138(n-1)] of this permutation are given by A127384 and A086625 shifted once right. The maximum cycles and LCM's of cycle sizes begin as 1, 1, 1, 2, 4, 4, 8, 8, 8, 8, 16, 16, 16, 16, ... A127302(a(n)) = A127302(n) holds for all n. A127388 shows a variant which is an involution.
Differs from A073289 and A122349 for the first time at n=54, where a(n)=54, while A073289(54) = A122349(54) = 61.
Showing 1-3 of 3 results.

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