Class CatalanSequence

java.lang.Object

org.episteme.core.mathematics.analysis.series.CatalanSequence

All Implemented Interfaces:

Function<Natural,Integer>, Function<Natural,Integer>, Relation<Natural,Integer>, IntegerSequence, Sequence<Integer>

public class CatalanSequence
extends Object
implements IntegerSequence

Catalan numbers: C(0)=1, C(n) = (2n)! / ((n+1)! * n!).

OEIS A000108: Catalan numbers.

Counts the number of:

• Binary trees with n internal nodes
• Ways to triangulate a convex (n+2)-gon
• Balanced parentheses sequences of length 2n

Since:

1.0

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Constructor Summary

Constructors

Constructor	Description
CatalanSequence()

Method Summary

Modifier and Type	Method	Description
Integer	get(Natural n)	Returns the n-th term of the sequence (0-indexed).
String	getCodomain()	Returns the codomain description.
String	getFormula()	Returns a formula or description of how terms are computed.
String	getName()	Returns a human-readable name for this sequence.
String	getOEISId()	Returns the OEIS (Online Encyclopedia of Integer Sequences) identifier.

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface Function

compose

Methods inherited from interface Function

andThen, compose, contains, evaluate, getBackend, isContinuous, isDifferentiable, setBackend

Methods inherited from interface IntegerSequence

getLong, getLong

Methods inherited from interface Sequence

apply, evaluate, get, getDomain

Constructor Details

CatalanSequence

public CatalanSequence()

Method Details

get

public Integer get(Natural n)

Description copied from interface: Sequence

Returns the n-th term of the sequence (0-indexed).

This is the canonical method using Episteme number types.

Specified by:

get in interface Sequence<Integer>

Parameters:

n - the index (n ≥ 0)

Returns:

a(n)

getOEISId

public String getOEISId()

Description copied from interface: Sequence

Returns the OEIS (Online Encyclopedia of Integer Sequences) identifier. For example, "A000045" for Fibonacci numbers.

Specified by:

getOEISId in interface Sequence<Integer>

Returns:

OEIS ID or null if not catalogued

getName

public String getName()

Description copied from interface: Sequence

Returns a human-readable name for this sequence.

Specified by:

getName in interface Sequence<Integer>

Returns:

sequence name

getFormula

public String getFormula()

Description copied from interface: Sequence

Returns a formula or description of how terms are computed.

Specified by:

getFormula in interface Sequence<Integer>

Returns:

mathematical formula or description

getCodomain

public String getCodomain()

Description copied from interface: Relation

Returns the codomain description.

Specified by:

getCodomain in interface Relation<Natural,Integer>

Returns:

codomain name