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 1-6 of 6 results.

A126317 Number of cycles in range [A014137(n-1)..A014138(n-1)] of permutation A125977/A125978.

Original entry on oeis.org

1, 1, 2, 3, 6, 16, 36, 79, 162, 316, 604, 1204, 2244
Offset: 0

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Author

Antti Karttunen, Jan 16 2007

Keywords

A126318 Maximum cycle size in range [A014137(n-1)..A014138(n-1)] of permutation A125977/A125978.

Original entry on oeis.org

1, 1, 1, 3, 3, 5, 11, 45, 257, 575, 2470, 10892, 30297
Offset: 0

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Author

Antti Karttunen, Jan 16 2007

Keywords

A126319 Least common multiple of all cycle sizes in range [A014137(n-1)..A014138(n-1)] of permutation A125977/A125978.

Original entry on oeis.org

1, 1, 1, 3, 3, 15, 33, 9061920, 1252445414220, 126032376305404800, 50110448042127911907268800, 13399946812028296616282674883512406948355335893125182077721607466200299913000
Offset: 0

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Author

Antti Karttunen, Jan 16 2007

Keywords

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.

A126312 Fixed points of permutation A071661/A071662.

Original entry on oeis.org

0, 1, 2, 3, 4, 8, 9, 22, 23, 30, 55, 64, 65, 98, 158, 196, 197, 318, 484, 625, 626, 687, 1042, 1549, 1973, 2055, 2056, 2376, 3471, 5113, 6558, 6917, 6918, 8191, 11763, 17268, 22277, 23713, 23714, 24331, 28360, 40491, 59362, 76942, 81754, 82499
Offset: 0

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Author

Antti Karttunen, Jan 16 2007

Keywords

Comments

Those i for which A071661(i)=i, i.e. for which A057163(A057164(i)) = A057164(A057163(i)). These appear to consist of just those general plane trees which are symmetric and will stay symmetric also after the underlying plane binary tree has been reflected, i.e. for which A057164(i)=i and A057164(A057163(i)) = A057163(i). See comments at A123050 and A080070. The sequence seems to give also the fixed points of the permutation A125977/A125978.

Links

A125980 Signature-permutation of a Catalan automorphism: A057163-conjugate of A125976.

Original entry on oeis.org

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

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Author

Antti Karttunen, Jan 02 2007

Keywords

Comments

This is self-inverse permutation (involution) of the nonnegative integers.

Links

Crossrefs

a(n) = A057163(A125976(A057163(n))) = A125977(A057163(n)) = A057163(A125978(n)).
Showing 1-6 of 6 results.

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