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 1-5 of 5 results.

A073202 Array of fix-count sequences for the table A073200.

Original entry on oeis.org

1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 0, 3, 0, 1, 1, 2, 8, 1, 0, 1, 1, 0, 20, 0, 0, 0, 1, 1, 5, 60, 2, 0, 1, 0, 1, 1, 0, 181, 0, 0, 0, 0, 0, 1, 1, 14, 584, 5, 0, 2, 0, 1, 2, 1, 1, 0, 1916, 0, 0, 0, 0, 0, 5, 0, 1, 1, 42, 6476, 14, 0, 5, 0, 0, 14, 1, 2, 1, 1, 0, 22210, 0, 0, 0, 0, 0, 42, 0, 1, 0, 1, 1
Offset: 0

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Author

Antti Karttunen, Jun 25 2002

Keywords

Comments

Each row of this table gives the counts of elements fixed by the Catalan bijection (given in the corresponding row of A073200) when it acts on A000108(n) structures encoded in the range [A014137(n-1)..A014138(n-1)] of the sequence A014486/A063171.

Links

  • A. Karttunen, Gatomorphisms (With the complete source and explanation)

Crossrefs

Cf. also A073201, A073203.
Few EIS-sequences which occur in this table. Only the first known occurrence(s) given (marked with ? if not yet proved/unclear):
Rows 0, 2, 4, etc.: "Aerated Catalan numbers" shifted right and prepended with 1 (Cf. A000108), Row 1: A073190, Rows 3, 5, 261, 2614, 2618, 17517, etc: A019590 but with offset 0 instead of 1 (means that the Catalan bijections like A073269, A073270, A057501, A057505, A057503 and A057161 never fix any Catalan structure of size larger than 1).
Row 6: A036987, Row 7: A000108, Rows 12, 14, 20, ...: A057546, Rows 16, 18: A034731, Row 41: A073268, Row 105: essentially A073267, Row 57, ..., 164: A001405, Row 168: A073192, Row 416: essentially A023359 ?, Row 10435: also A036987.

A073286 Permutation of natural numbers induced by the composition of the Catalan bijections A069770 & A069767.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jun 25 2002

Keywords

Links

Crossrefs

Inverse permutation: A073287. Occurs for first time in A073200 as row 41. Counts of the fixed elements: A073268.

Formula

a(n) = A069770(A069767(n)).

A073287 Permutation of natural numbers induced by the composition of the Catalan bijections A069768 & A069770.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jun 25 2002

Keywords

Links

Crossrefs

Inverse permutation: A073286. Occurs for first time in A073200 as row 69. Counts of the fixed elements: A073268.

Formula

a(n) = A069768(A069770(n)).

A130341 Row 3 of A122203.

Original entry on oeis.org

0, 1, 2, 3, 5, 4, 6, 7, 8, 12, 13, 11, 10, 9, 15, 14, 16, 17, 18, 19, 20, 21, 22, 31, 32, 34, 35, 36, 30, 33, 29, 26, 27, 28, 25, 24, 23, 40, 41, 39, 38, 37, 43, 42, 44, 45, 46, 47, 48, 49, 50, 52, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 87, 88, 90, 91, 92, 96, 97
Offset: 0

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Author

Antti Karttunen, Jun 05 2007

Keywords

Comments

The signature-permutation of the Catalan automorphism which is derived from the third non-recursive Catalan automorphism *A089850 with recursion schema SPINE (see A122203 for the definition). This automorphism is also produced when automorphism *A069767 is applied to the right-hand side subtree of the given binary tree, with the left side left intact.

Links

Crossrefs

Inverse: A130342. a(n) = A069767(A069770(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 A089404 and A073268. Cf. also A073286.

A130342 Row 3 of A122204.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jun 05 2007

Keywords

Comments

The signature-permutation of the Catalan automorphism which is derived from the third non-recursive Catalan automorphism *A089850 with recursion schema ENIPS (see A122204 for the definition). This automorphism is also produced when automorphism *A069768 is applied to the right-hand side subtree of the given binary tree, with the left side left intact.

Links

Crossrefs

Inverse: A130341. a(n) = A069770(A069768(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 A089404 and A073268. Cf. also A073287.
Showing 1-5 of 5 results.

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