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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A183758 Unlabeled super-Catalan numbers: patterns of nonintersecting chords joining unlabeled points on a flippable circle.

Original entry on oeis.org

1, 1, 2, 5, 12, 44, 176, 809, 3883, 19265
Offset: 0

Views

Author

David Scambler, Jan 06 2011

Keywords

Comments

Interpret the super-Catalan sequence (A001003) as follows: Ways to insert parentheses in a string of n+1 symbols. The parentheses must be balanced but there is no restriction on the number of pairs of parentheses. The number of letters inside a pair of parentheses must be at least 2. Parentheses enclosing the whole string are ignored. Now picture the x's and parentheses as equally spaced unlabeled points on a circle with chords joining paired parentheses and x's having no chord. Circles thus produced may have n+1, n+3, ..., 3*n-1 points and up to n-1 chords. The circle may be rotated and flipped over. a(n) is the count of unique patterns.

Examples

			A183757(3) = 6: (xx)xx, (xx)(xx), (xxx)x, ((xx)x)x, x(x(xx)), xxxx and removing the reflected pattern x(x(xx)) leaves a(3) = 5.

Crossrefs

Cf. A001003 super-Catalan numbers. A183757 similar but counts reflections. A183760 this sequence decomposed by number of chords in the circles.

A183759 Unlabeled super-Catalan numbers: patterns of nonintersecting chords joining unlabeled points on a circle, triangle decomposed by number of chords.

Original entry on oeis.org

1, 1, 1, 1, 2, 3, 1, 2, 7, 7, 1, 3, 15, 33, 22, 1, 3, 24, 94, 136, 66, 1, 4, 41, 218, 525, 552, 217, 1, 4, 57, 440, 1517, 2673, 2233, 715, 1, 5, 86, 804, 3748, 9439, 12917, 8807, 2438
Offset: 1

Views

Author

David Scambler, Jan 06 2011

Keywords

Comments

Decomposition of A183757 by number of chords (pairs of parentheses). Row sums are A183757. See A183757 for description.
Triangle is
1
1 1
1 2 3
1 2 7 7
1 3 15 33 22
1 3 24 94 136 66
...
Right diagonal is apparently A007595.

Crossrefs

Decomposition of A183757.
Cf. analogous decomposition of super-Catalan numbers in triangle A033282.
Showing 1-2 of 2 results.

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

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