A074679 -id:A074679 - cp's OEIS frontend

A123495 Signature permutation of a nonrecursive Catalan automorphism: row 65518 of table A089840.

0, 1, 3, 2, 6, 7, 8, 4, 5, 14, 15, 16, 17, 18, 21, 22, 19, 9, 10, 20, 11, 12, 13, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 58, 59, 62, 63, 64, 56, 60, 51, 23, 24, 52, 25, 26, 27, 57, 61, 53, 28, 29, 54, 30, 31, 32, 55, 33, 34, 35, 36, 107, 108, 109, 110, 111

Offset: 0

Antti Karttunen, Oct 11 2006

nonn

A. Karttunen, Prolog-program which illustrates the construction of this and other similar nonrecursive Catalan automorphisms.
Index entries for signature-permutations of Catalan automorphisms

Inverse: A123496. a(n) = A082351(A069770(n)). Row 65518 of A089840. Used to construct automorphism *A082357. Cf. A069770 and A074679.

A129609 Signature-permutation of a Catalan automorphism, row 65167 of A089840.

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, May 22 2007

nonn

Automorphism *A074679 = ENIPS(*A129609). See the definition given in A122204.

Inverse: A129610.

A129610 Signature-permutation of a Catalan automorphism, row 65352 of A089840.

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, May 22 2007

nonn

Automorphism *A074680 = SPINE(*A129610). See the definition given in A122203.

Inverse: A129609.

A153834 Index sequence to A089840: position of A089840(n) when applied to the right hand side subtree.

Original entry on oeis.org

0, 3, 23, 27, 29, 33, 35, 46, 50, 52, 56, 58, 3655, 3659, 3667, 3677, 3681, 3747, 3751, 3759, 3763, 3771, 277, 281, 283, 287, 289, 299, 301, 305, 307, 311, 313, 323, 325, 329, 331, 335, 337, 347, 349, 353, 355, 359, 361, 396, 400, 402, 406, 408, 418, 420

Offset: 0

Antti Karttunen, Jan 07 2009

nonn

The comments at A123694 concerning counts of fixed points apply also here.

			When A089840(1) = A069770 (swap binary tree sides) is applied to the right subtree of a binary tree, we get A089850 = A089840(3), thus a(1)=3. When A089840(12) = A074679 is applied to the right subtree of a binary tree, we get A154121 = A089840(3655), thus a(12)=3655.

A. Karttunen, C-program for computing the initial terms of this sequence

a(n) < A123694(n) for all n > 0. Used to construct A153832 and A153833.

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

Antti Karttunen, Dec 05 2003

nonn

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.

A. Karttunen, C-program for computing the initial terms of this sequence

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].

A085167 Permutation of natural numbers induced by the Catalan bijection gma085167 acting on symbolless S-expressions encoded by A014486/A063171.

Original entry on oeis.org

0, 1, 3, 2, 5, 8, 7, 4, 6, 10, 13, 15, 18, 22, 12, 21, 17, 9, 11, 20, 14, 16, 19, 24, 27, 29, 32, 36, 38, 41, 43, 46, 50, 52, 55, 59, 64, 26, 35, 40, 49, 63, 31, 58, 45, 23, 25, 48, 28, 30, 33, 34, 62, 54, 37, 39, 57, 42, 44, 47, 61, 51, 53, 56, 60, 66, 69, 71, 74, 78

Offset: 0

Antti Karttunen, Jun 23 2003

nonn

Antti Karttunen, Gatomorphisms (With the complete Scheme source)
Index entries for signature-permutations induced by Catalan automorphisms

Inverse: A085168. a(n) = A085159(A069770(n)). Occurs in A073200. Cf. also A074679, A074680, A085203.

Number of cycles in range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right: A001683. [To be checked.].

cp's OEIS Frontend

A123495 Signature permutation of a nonrecursive Catalan automorphism: row 65518 of table A089840.

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A129609 Signature-permutation of a Catalan automorphism, row 65167 of A089840.

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A129610 Signature-permutation of a Catalan automorphism, row 65352 of A089840.

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A153834 Index sequence to A089840: position of A089840(n) when applied to the right hand side subtree.

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

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A085167 Permutation of natural numbers induced by the Catalan bijection gma085167 acting on symbolless S-expressions encoded by A014486/A063171.

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