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 1-4 of 4 results.

A080981 A014486-encodings of the trees whose interior zigzag-tree (Stanley's c) is branch-reduced (in the sense defined by Donaghey).

Original entry on oeis.org

0, 2, 10, 12, 44, 50, 52, 178, 180, 204, 210, 216, 228, 716, 722, 728, 740, 818, 820, 844, 866, 868, 872, 914, 920, 932, 2866, 2868, 2892, 2914, 2916, 2920, 2962, 2968, 2980, 3276, 3282, 3288, 3300, 3378, 3380, 3468, 3474, 3480, 3490, 3492, 3504, 3528, 3660
Offset: 0

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Author

Antti Karttunen, Mar 02 2003

Keywords

Comments

Donaghey defines (on page 82 of his paper) the branch-reduced zigzag-trees as those zigzag-trees which do not contain longer than one-edge branches, where a branch is a maximal connected set of edges slanted to the same direction, with no perpendicular edges emanating from its middle. These form the primitive elements of the automorphism A057505/A057506.

Links

Crossrefs

a(n) = A014486(A080980(n)). Cf. A080968, A080971. These trees are enumerated by A005554.

Formula

a(n) = A014486(A080980(n)).

A080968 Orbit size of each branch-reduced tree encoded by A080981(n) under Donaghey's "Map M" Catalan automorphism.

Original entry on oeis.org

1, 1, 2, 2, 3, 3, 3, 6, 6, 6, 6, 6, 6, 3, 2, 3, 5, 3, 5, 5, 5, 5, 3, 3, 2, 3, 6, 24, 24, 24, 24, 6, 24, 24, 24, 6, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 6, 24, 24, 24, 24, 24, 6, 24, 24, 6, 3, 18, 9, 24, 18, 18, 9, 18, 9, 18, 18, 3, 24, 15, 15, 24, 24, 18, 15, 15, 24, 3, 24, 24, 15, 15, 24
Offset: 0

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Author

Antti Karttunen, Mar 02 2003

Keywords

Comments

This is the size of the cycle containing A080980(n) in the permutations A057505/A057506.
If the conjecture given in A080070 is true, then this sequence contains only six 2's. Questions: are there any (other) values with finite number of occurrences? Which primes will eventually appear?

Crossrefs

Cf. A080969, A080972.

Formula

a(n) = A080967(A080980(n))

A080970 A014486-indices of the trees whose interior zigzag-tree (Stanley's c) is not branch-reduced (in the sense defined by Donaghey).

Original entry on oeis.org

4, 8, 9, 10, 13, 14, 17, 19, 21, 22, 23, 24, 25, 26, 27, 28, 31, 33, 35, 36, 37, 38, 41, 42, 44, 45, 46, 50, 51, 52, 54, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 83, 84, 86, 87, 88, 92, 93, 94, 96, 98, 100, 101, 102, 103
Offset: 0

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Author

Antti Karttunen, Mar 02 2003

Keywords

Links

Crossrefs

Cf. A014486, A080300, A080971.
See comment at A080971. Complement of A080980.

Formula

a(n) = A080300(A080971(n)).

A080979 Each tree encoded in A014486 mapped to the corresponding branch-reduced zigzag-tree (positions in A014486).

Original entry on oeis.org

0, 1, 2, 3, 2, 5, 6, 7, 3, 2, 5, 11, 12, 5, 6, 15, 16, 7, 18, 6, 20, 7, 3, 2, 5, 11, 12, 5, 11, 29, 30, 12, 32, 11, 34, 12, 5, 6, 15, 39, 40, 15, 16, 43, 16, 7, 18, 47, 48, 49, 18, 6, 15, 53, 20, 55, 16, 57, 7, 18, 6, 20, 20, 7, 3, 2, 5, 11, 12, 5, 11, 29, 30, 12, 32, 11, 34, 12, 5, 11, 29
Offset: 0

Views

Author

Antti Karttunen, Mar 02 2003

Keywords

Comments

For trees which are already branch-reduced we have a(n)=n, where n is one of A080980.

Links

Crossrefs

Same sequence sorted, with duplicates removed: A080980. Cf. A080293.
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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