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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A123497 Signature permutation of a nonrecursive Catalan automorphism: row 1655089 of table A089840.

Original entry on oeis.org

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

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Author

Antti Karttunen, Oct 11 2006

Keywords

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Crossrefs

Inverse: A123498. Row 1655089 of A089840. Used to construct automorphism *A123501. A074680(n) = A083927(a(A057123(n))).

A123498 Signature permutation of a nonrecursive Catalan automorphism: row 1654249 of table A089840.

Original entry on oeis.org

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

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Author

Antti Karttunen, Oct 11 2006

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Links

Crossrefs

Inverse: A123497. Row 1654249 of A089840. Used to construct automorphism *A123502. A074679(n) = A083927(a(A057123(n))).

A073196 Permutation of natural numbers induced by the Catalan bijection gmA073196 acting on the parenthesizations as ordered by A014486.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jun 25 2002

Keywords

Comments

Is there an equivalent Catalan bijection in A073200?

Links

Crossrefs

Inverse permutation: A073197. The car/cdr-flipped conjugate of A073207, i.e. A073196(n) = A057163(A073207(A057163(n))). Cf. also A073194-A073199.
The scheme functions gma072796! and gma072797! referred to below are given in A072796 and A072797.

A073284 Permutation of natural numbers induced by the Catalan bijection gma073284! acting on the parenthesizations encoded by A014486.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 5, 7, 8, 9, 11, 14, 16, 19, 10, 15, 12, 17, 20, 13, 18, 21, 22, 23, 25, 28, 30, 33, 37, 39, 42, 44, 47, 51, 53, 56, 60, 24, 29, 38, 43, 52, 26, 40, 31, 45, 48, 32, 54, 57, 61, 27, 41, 34, 46, 55, 35, 49, 58, 62, 36, 50, 59, 63, 64, 65, 67, 70, 72, 75, 79, 81
Offset: 0

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Author

Antti Karttunen, Jun 25 2002

Keywords

Links

Crossrefs

Inverse permutation: A073285. Occurs for first time in A073200 as row 20.
The scheme function gma072796! referred to below given in A072796.

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.

A073195 Permutation of natural numbers induced by the Catalan bijection gmA073195 acting on the parenthesizations as ordered by A014486.

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 5, 6, 8, 9, 16, 10, 17, 20, 11, 18, 12, 14, 21, 13, 15, 19, 22, 23, 44, 24, 42, 43, 25, 57, 26, 45, 53, 27, 46, 54, 61, 28, 47, 29, 48, 55, 30, 49, 31, 37, 56, 32, 38, 58, 62, 33, 50, 34, 39, 59, 35, 40, 51, 63, 36, 41, 52, 60, 64, 65, 126, 66, 128, 131, 67
Offset: 0

Views

Author

Antti Karttunen, Jun 25 2002

Keywords

Comments

Is there an equivalent Catalan bijection in A073200?

Links

Crossrefs

Inverse permutation: A073194. The car/cdr-flipped conjugate of A073206, i.e. A073195(n) = A057163(A073206(A057163(n))). Cf. also A073194-A073199.
The scheme functions gma072796! and gma072797! referred to below are given in A072796 and A072797.

A073198 Permutation of natural numbers induced by the Catalan bijection gmA073198 acting on the parenthesizations as ordered by A014486.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 7, 5, 8, 9, 14, 16, 11, 19, 17, 18, 10, 12, 15, 20, 13, 21, 22, 23, 37, 42, 30, 51, 44, 47, 28, 25, 39, 53, 33, 56, 60, 45, 46, 48, 49, 50, 26, 29, 24, 31, 40, 38, 43, 32, 52, 54, 55, 27, 34, 41, 57, 35, 58, 59, 61, 36, 62, 63, 64, 65, 107, 121, 70, 149, 126
Offset: 0

Views

Author

Antti Karttunen, Jun 25 2002

Keywords

Comments

Is there an equivalent Catalan bijection in A073200?

Links

Crossrefs

Inverse permutation: A073199. The car/cdr-flipped conjugate of A073209, i.e. A073198(n) = A057163(A073209(A057163(n))). Cf. also A073194-A073197.
The scheme functions gma072796! and gma072797! referred to below are given in A072796 and A072797.

A073206 Permutation of natural numbers induced by the Catalan bijection gmA073206 acting on the parenthesizations as ordered by A014486.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 7, 5, 8, 9, 14, 16, 10, 19, 17, 18, 12, 11, 13, 20, 21, 15, 22, 23, 37, 42, 24, 51, 44, 47, 26, 25, 27, 53, 56, 38, 60, 45, 46, 48, 49, 50, 31, 32, 30, 28, 33, 34, 35, 39, 36, 54, 55, 57, 58, 59, 40, 29, 43, 52, 61, 62, 63, 41, 64, 65, 107, 121, 66, 149, 126
Offset: 0

Views

Author

Antti Karttunen, Jun 25 2002

Keywords

Comments

Is there an equivalent Catalan bijection in A073200?

Links

Crossrefs

Inverse permutation: A073205. The car/cdr-flipped conjugate of A073195, i.e. A073206(n) = A057163(A073195(A057163(n))). Cf. also A073207-A073210.
The scheme functions gma072796! and gma072797! referred to below are given in A072796 and A072797.

A073209 Permutation of natural numbers induced by the Catalan bijection gmA073209 acting on the parenthesizations as ordered by A014486.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jun 25 2002

Keywords

Comments

Is there an equivalent Catalan bijection in A073200?

Links

Crossrefs

Inverse permutation: A073210. The car/cdr-flipped conjugate of A073198, i.e. A073209(n) = A057163(A073198(A057163(n))). Cf. also A073205-A073208.
The scheme functions gma072796! and gma072797! referred to below are given in A072796 and A072797.

A073285 Permutation of natural numbers induced by the Catalan bijection gma073285! acting on the parenthesizations encoded by A014486.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 5, 7, 8, 9, 14, 10, 16, 19, 11, 15, 12, 17, 20, 13, 18, 21, 22, 23, 37, 24, 42, 51, 25, 38, 26, 44, 47, 27, 53, 56, 60, 28, 39, 29, 43, 52, 30, 40, 31, 45, 54, 32, 46, 57, 61, 33, 41, 34, 48, 55, 35, 49, 58, 62, 36, 50, 59, 63, 64, 65, 107, 66, 121, 149, 67
Offset: 0

Views

Author

Antti Karttunen, Jun 25 2002

Keywords

Links

Crossrefs

Inverse permutation: A073284.
The scheme function gma072796! referred to below given in A072796.
Previous Showing 31-40 of 49 results. Next

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