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.

Previous Showing 11-20 of 20 results.

A122302 Row 1 of A122284, row 15 of A122202.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Sep 01 2006

Keywords

Comments

The signature-permutation of the automorphism which is derived from the first non-recursive automorphism *A069770 with recursion schema NEPEED (see A122284 for the definition), or equivalently, derived from the fifteenth non-recursive automorphism *A089859 with recursion schema KROF (see A122202 for the definition).

Links

Crossrefs

Inverse: A122301.

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.

A122353 Row 15 of A122201.

Original entry on oeis.org

0, 1, 3, 2, 7, 8, 6, 5, 4, 18, 17, 20, 21, 22, 16, 19, 15, 12, 13, 14, 11, 10, 9, 49, 50, 48, 46, 45, 55, 54, 57, 59, 58, 61, 62, 63, 64, 47, 44, 53, 56, 60, 43, 52, 40, 32, 31, 41, 34, 35, 36, 42, 51, 39, 30, 33, 38, 29, 26, 27, 37, 28, 25, 24, 23, 143, 142, 146, 147, 148
Offset: 0

Views

Author

Antti Karttunen, Sep 01 2006

Keywords

Comments

The signature-permutation of the automorphism which is derived from the fifteenth non-recursive automorphism *A089859 with recursion schema FORK (see A122201 for the definition).

Links

Crossrefs

Inverse: A122354.

A089831 Triangle T(n,m) (read as T(1,1); T(2,1), T(2,2); T(3,1), T(3,2), T(3,3);) Number of distinct non-recursive Catalan Automorphisms whose minimum clause-representation requires examination of n nodes in total, divided into m non-default clauses.

Original entry on oeis.org

1, 10, 0, 115, 10, 0, 1666, 139, 0, 0, 30198, 2570, 0, 0, 0, 665148, 47878, 904, 0, 0, 0, 17296851, 1017174, 20972, 0, 0, 0, 0
Offset: 1

Views

Author

Antti Karttunen, Dec 05 2003

Keywords

Examples

			...... Triangle............................ Row sums
........1........................................1
.......10.......0...............................10
......115......10...0..........................125 = 5^3
.....1666.....139...0....0....................1805 = 5*19^2
....30198....2570...0....0...0...............32768 = 32^3 = 8^5
...665148...47878...904..0...0...0..........713930
.17296851.1017174.20972..0...0...0...0....18334997
T(1,1)=1, as there is just one non-identity, non-recursive Catalan bijection with a single non-default clause opening a single node, namely A089840[1]=A069770.
T(2,1)=10, as there are the following non-recursive Catalan bijections (rows 2-11 of A089840): A072796, A089850, A089851, A089852, A089853, A089854, A072797, A089855, A089856, A089857, whose minimum clause-representation consists of a single non-default clause that opens two nodes.
T(3,2)=10, as there are the following non-recursive Catalan bijections (rows 12-21 of A089840): A074679, A089858, A073269, A089859, A089860, A074680, A089861, A073270, A089862, A089863, whose minimum clause-representation consists of a two non-default clauses with total 3 nodes opened.

Links

Crossrefs

First column: A089833. Row sums: A089832. Row sums excluding the first column: A089834.

A129611 Signature-permutation of a Catalan automorphism, row 169 of A089840.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, May 22 2007

Keywords

Comments

Automorphism *A089859 = ENIPS(*A129611). See the definition given in A122204.

Links

Crossrefs

Inverse: A129612.

A129612 Signature-permutation of a Catalan automorphism, row 251 of A089840.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, May 22 2007

Keywords

Comments

Automorphism *A089863 = SPINE(*A129612). See the definition given in A122203.

Links

Crossrefs

Inverse: A129611. Differs from A082345 for the first time at n=49, where A082345(49)=27, while a(49)=26.

A122327 Row 15 of A122283.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Sep 01 2006

Keywords

Comments

The signature-permutation of the automorphism which is derived from the fifteenth non-recursive automorphism *A089859 with recursion schema DEEPEN (see A122283 for the definition).

Links

Crossrefs

Inverse: A122328.

A130397 Signature permutation of a Catalan automorphism: row 15 of A130400.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jun 11 2007

Keywords

Comments

The signature-permutation of the Catalan automorphism which is derived from the 15th non-recursive Catalan automorphism *A089859 with recursion schema INORDER (see A130400 for the definition).

Links

Crossrefs

Inverse: A130398.

A089842 Order of each element (row) in A089840, 0 if not finite.

Original entry on oeis.org

1, 2, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 2, 2, 3, 2, 3, 2, 2, 3, 4, 3, 4, 2, 3, 3, 4, 2, 4, 2, 3, 2, 4, 3, 4, 2, 2, 3, 2, 3, 2, 2, 3, 4, 3, 4, 2, 3, 3, 4, 2, 4, 2, 3, 2, 4, 3, 4, 2, 2, 3, 2, 3, 2, 2, 3, 4, 3, 4, 2, 3, 3, 4, 2, 4, 2, 3, 2, 4, 3, 4, 2, 2, 3, 2, 3, 2, 2, 3, 4, 3, 4
Offset: 0

Views

Author

Antti Karttunen, Dec 05 2003

Keywords

Comments

If a(n) is nonzero, then the n-th non-recursive Catalan Automorphism in A089840 does not have orbits (cycles) larger than that and the corresponding LCM-sequence will set to a constant sequence a(n),a(n),a(n),a(n),... E.g. A089840[4] = A089851 is obtained by rotating three subtrees cyclically and its LCM-sequence begins as 1,1,1,3,3,3,3,3,3,3,3,... (a(4)=3). Similarly, A089840[15] = A089859, whose LCM-sequence begins as 1,1,2,4,4,4,4,4,4,4,4,.... (a(15)=4). In contrast, the Max. cycle and LCM-sequence (A089410) of A089840[12] (= A074679) exhibits genuine growth, thus a(12)=0.

Links

Crossrefs

Note that the terms 1-23 of A060131: 2, 2, 3, 2, 3, 2, 2, 3, 4, 3, 4, 2, 3, 3, 4, 2, 4, 2, 3, 2, 4, 3, 4 repeat here at positions [22..44], [45..67], [68..90], [91..113], [114..136].

A122340 Row 15 of A122284.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Sep 01 2006

Keywords

Comments

The signature-permutation of the automorphism which is derived from the fifteenth non-recursive automorphism *A089859 with recursion schema NEPEED (see A122284 for the definition).

Links

Crossrefs

Inverse: A122339.
Previous Showing 11-20 of 20 results.

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