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 1-10 of 47 results. Next

A122285 Signature permutations of ENIPS-transformations of Catalan automorphisms in table A122203.

Original entry on oeis.org

0, 1, 0, 2, 1, 0, 3, 3, 1, 0, 4, 2, 2, 1, 0, 5, 8, 3, 2, 1, 0, 6, 7, 4, 3, 2, 1, 0, 7, 6, 6, 5, 3, 2, 1, 0, 8, 5, 5, 4, 5, 3, 2, 1, 0, 9, 4, 7, 6, 6, 6, 3, 2, 1, 0, 10, 22, 8, 7, 4, 5, 6, 3, 2, 1, 0, 11, 21, 9, 8, 7, 4, 4, 4, 3, 2, 1, 0, 12, 20, 14, 13, 8, 7, 5, 5, 4, 3, 2, 1, 0, 13, 18, 11, 12, 13
Offset: 0

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Author

Antti Karttunen, Sep 01 2006, Jun 20 2007

Keywords

Comments

Row n is the signature permutation of the Catalan automorphism which is obtained from the n-th automorphism in the table A122203 with the recursion scheme "ENIPS", or equivalently row n is obtained as ENIPS(SPINE(n-th row of A089840)). See A122203 and A122204 for the description of SPINE and ENIPS. Each row occurs only once in this table. Inverses of these permutations can be found in table A122286. This table contains also all the rows of A122204 and A089840.

References

  • A. Karttunen, paper in preparation, draft available by e-mail.

Links

Crossrefs

The first 22 rows of this table: row 0 (identity permutation): A001477, 1: A082348, 2: A057508, 3: A131141, 4: A131143, 5: A131145, 6: A131147, 7: A131173, 8: A131169, 9: A131149, 10: A131151, 11: A131153, 12: A131171, 13: A131155, 14: A131157, 15: A131159, 16: A131161, 17: A057503, 18: A131163, 19: A131165, 20: A131167, 21: A069768. Other rows: row 251: A130360, 3608: A130339, 3613: A057510, 65352: A074686.
See also tables A089840, A122200, A122201-A122204, A122283-A122284, A122286-A122288, A122289-A122290, A130400-A130403. As a sequence differs from A122286 for the first time at n=92, where a(n)=18, while A122286(n)=17.

A122288 Signature permutations of KROF-transformations of Catalan automorphisms in table A122203.

Original entry on oeis.org

0, 1, 0, 2, 1, 0, 3, 3, 1, 0, 4, 2, 2, 1, 0, 5, 8, 3, 2, 1, 0, 6, 7, 4, 3, 2, 1, 0, 7, 6, 6, 5, 3, 2, 1, 0, 8, 4, 5, 4, 5, 3, 2, 1, 0, 9, 5, 7, 6, 6, 6, 3, 2, 1, 0, 10, 22, 8, 7, 4, 5, 6, 3, 2, 1, 0, 11, 21, 9, 8, 7, 4, 4, 4, 3, 2, 1, 0, 12, 20, 14, 13, 8, 7, 5, 5, 4, 3, 2, 1, 0, 13, 17, 11, 12, 13
Offset: 0

Views

Author

Antti Karttunen, Sep 01 2006, Jun 20 2007

Keywords

Comments

Row n is the signature permutation of the Catalan automorphism which is obtained from the n-th automorphism in the table A122203 with the recursion scheme "KROF", or equivalently row n is obtained as KROF(SPINE(n-th row of A089840)). See A122202 and A122203 for the description of KROF and SPINE. Moreover, each row of A122288 can be obtained as the "NEPEED" transform of the corresponding row in A122285. (See A122284 for the description of NEPEED). Each row occurs only once in this table. Inverses of these permutations can be found in table A122287. This table contains also all the rows of A122202 and A089840.

References

  • A. Karttunen, paper in preparation, draft available by e-mail.

Links

Crossrefs

The first 22 rows of this table: row 0 (identity permutation): A001477, 1: A069768, 2: A057164, 3: A130981, 4: A130983, 5: A130982, 6: A130984, 7: A130985, 8: A130987, 9: A130989, 10: A130991, 11: A130993, 12: A131009, 13: A130995, 14: A130997, 15: A130999, 16: A131001, 17: A057505, 18: A131003, 19: A131005, 20: A131007, 21: A057163. Other rows: 251: A122354, 3613: A057512, 65352: A074682.
See also tables A089840, A122200, A122201-A122204, A122283-A122284, A122285-A122286, A122289-A122290, A130400-A130403.

A130402 Signature permutations of ENIPS-transformations of A057163-conjugates of Catalan automorphisms in table A122203.

Original entry on oeis.org

0, 1, 0, 2, 1, 0, 3, 3, 1, 0, 4, 2, 2, 1, 0, 5, 7, 3, 2, 1, 0, 6, 8, 4, 3, 2, 1, 0, 7, 6, 5, 4, 3, 2, 1, 0, 8, 4, 7, 5, 4, 3, 2, 1, 0, 9, 5, 6, 6, 5, 4, 3, 2, 1, 0, 10, 17, 8, 8, 8, 5, 4, 3, 2, 1, 0, 11, 18, 9, 7, 6, 8, 5, 5, 3, 2, 1, 0, 12, 20, 10, 9, 7, 7, 7, 4, 4, 3, 2, 1, 0, 13, 22, 12, 10, 9, 6
Offset: 0

Views

Author

Antti Karttunen, Jun 11 2007

Keywords

Comments

Row n is the signature permutation of the Catalan automorphism which is obtained from A057163-conjugate of the n-th automorphism in the table A122203 with the recursion scheme "ENIPS", i.e. row n is obtained as ENIPS(A057163 o SPINE(A089840[n]) o A057163). See A122203 and A122204 for the description of SPINE and ENIPS. Each row occurs only once in this table. Inverses of these permutations can be found in table A130403. This table contains also all the rows of A122204 and A089840.

Crossrefs

Cf. The first 22 rows of this table: row 0 (identity permutation): A001477, 1: A082346, 2: A130935, 3: A073289, 4: A130937, 5: A130939, 6: A130941, 7: A130943, 8: A130945, 9: A130947, 10: A130949, 11: A130951, 12: A074687, 13: A130953, 14: A130955, 15: A130957, 16: A130959, 17: A057162, 18: A130961, 19: A130963, 20: A130965, 21: A069768. Other rows: 251: A069770, 3613: A082340, 65352: A057502.
Cf. also tables A089840, A122201-A122204, A122285-A122286, A130400-A130401.
Cf. As a sequence differs from A130403 for the first time at n=92, where a(n)=22, while A130403(n)=21.

A122282 Row 1 of A122200, row 7 of A122203 and A122204.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Sep 01 2006

Keywords

Comments

An involution of nonnegative integers.
The signature-permutation of the automorphism which is derived from the first non-recursive automorphism *A069770 with the recursion schema RIBS (see A122200), or alternatively, derived from the seventh non-recursive automorphism *A089854 with recursion scheme SPINE or ENIPS (see A122203, A122204 for their definitions).

Links

Crossrefs

The number of fixed points in range [A014137(n-1)..A014138(n-1)] of this permutation is given by INVERT transform of "aerated" Catalan numbers [1, 1, 0, 1, 0, 2, 0, 5, 0, 14, 0, 42, ...].

A123715 Signature permutation of a Catalan automorphism: row 79361 of table A122203.

Original entry on oeis.org

0, 1, 2, 3, 4, 8, 6, 7, 5, 9, 13, 20, 21, 22, 14, 19, 16, 17, 18, 15, 11, 12, 10, 23, 27, 34, 35, 36, 54, 55, 57, 58, 59, 61, 62, 63, 64, 37, 41, 53, 56, 60, 42, 51, 44, 45, 46, 47, 48, 49, 50, 43, 52, 39, 28, 33, 40, 30, 31, 32, 38, 29, 25, 26, 24, 65, 69, 76, 77, 78, 96, 97
Offset: 0

Views

Author

Antti Karttunen, Oct 11 2006

Keywords

Comments

This is the signature-permutation of Catalan automorphism which is derived from nonrecursive Catalan automorphism *A123492 with the recursion schema SPINE (defined in A122203).

Links

Crossrefs

Inverse: A123716. Row 79361 of A122203.

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

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 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.

A130349 Row 9 of A122203.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 7, 8, 6, 9, 10, 12, 13, 11, 17, 18, 20, 21, 22, 16, 19, 14, 15, 23, 24, 26, 27, 25, 31, 32, 34, 35, 36, 30, 33, 28, 29, 45, 46, 48, 49, 50, 54, 55, 57, 58, 59, 61, 62, 63, 64, 44, 47, 53, 56, 60, 42, 51, 37, 38, 43, 52, 40, 41, 39, 65, 66, 68, 69, 67, 73, 74
Offset: 0

Views

Author

Antti Karttunen, Jun 05 2007

Keywords

Comments

The signature-permutation of the Catalan automorphism which is derived from the ninth non-recursive Catalan automorphism *A089855 with recursion schema SPINE (see A122203 for the definition).

Links

Crossrefs

Inverse: A130350. Differs from A130354 for the first time at n=39, where a(39)=48, while A130354(39)=49.

A130353 Row 11 of A122203.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 8, 6, 7, 9, 10, 13, 11, 12, 21, 22, 19, 14, 15, 20, 16, 17, 18, 23, 24, 27, 25, 26, 35, 36, 33, 28, 29, 34, 30, 31, 32, 58, 59, 62, 63, 64, 56, 60, 51, 37, 38, 52, 41, 39, 40, 57, 61, 53, 42, 43, 54, 44, 45, 46, 55, 47, 48, 49, 50, 65, 66, 69, 67, 68, 77, 78
Offset: 0

Views

Author

Antti Karttunen, Jun 05 2007

Keywords

Comments

The signature-permutation of the Catalan automorphism which is derived from the eleventh non-recursive Catalan automorphism *A089857 with recursion schema SPINE (see A122203 for the definition).

Links

Crossrefs

Inverse: A130354. Differs from A130350 for the first time at n=39, where A130350(39)=64, while a(39)=62.

A130359 Row 15 of A122203.

Original entry on oeis.org

0, 1, 3, 2, 8, 7, 6, 5, 4, 21, 22, 20, 17, 18, 19, 16, 15, 13, 12, 14, 11, 10, 9, 58, 59, 62, 63, 64, 57, 61, 54, 45, 46, 55, 48, 49, 50, 56, 60, 53, 44, 47, 52, 43, 41, 35, 36, 40, 34, 31, 32, 51, 42, 39, 33, 30, 38, 29, 27, 26, 37, 28, 25, 24, 23, 170, 171, 174, 175, 176
Offset: 0

Views

Author

Antti Karttunen, Jun 05 2007

Keywords

Comments

The signature-permutation of the Catalan automorphism which is derived from the fifteenth non-recursive Catalan automorphism *A089859 with recursion schema SPINE (see A122203 for the definition).

Links

Crossrefs

Inverse: A130360.

A130343 Row 4 of A122203.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jun 05 2007

Keywords

Comments

The signature-permutation of the Catalan automorphism which is derived from the fourth non-recursive Catalan automorphism *A089851 with recursion schema SPINE (see A122203 for the definition).

Links

Crossrefs

Inverse: A130344.
Showing 1-10 of 47 results. Next

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