isLinearRecurrenceOfOrder
P46243
predicate
Indicates that one sequence or function is defined by a linear recurrence relation of a specified order, where each term is a linear combination of a fixed number of preceding terms.
All labels observed (2)
| Label | Occurrences |
|---|---|
| recurrenceRelation | 14 |
| isLinearRecurrenceOfOrder canonical | 1 |
Description generation (PDg)
The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.
Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning. # Instructions Focus on describing the relationship, not the entities themselves. # Response Format Begin the description with \' Indicates...\'
Input
Predicate: isLinearRecurrenceOfOrder
Generated description
Indicates that one sequence or function is defined by a linear recurrence relation of a specified order, where each term is a linear combination of a fixed number of preceding terms.
Sample triples (15)
| Subject | Object |
|---|---|
| Fibonacci sequence | 2 ⓘ |
| Bernoulli numbers | \sum_{k=0}^{n} {n+1 \choose k} B_k = 0 for n \ge 1 via predicate surface "recurrenceRelation" ⓘ |
| Pochhammer symbol | (a)_{n+1} = (a+n)(a)_n via predicate surface "recurrenceRelation" ⓘ |
| Pochhammer symbol | (a)_n = a(a+1)_{n-1} via predicate surface "recurrenceRelation" ⓘ |
| Bernoulli polynomials | B_0(x) = 1 via predicate surface "recurrenceRelation" ⓘ |
| Bernoulli polynomials | B_n'(x) = n B_{n-1}(x) via predicate surface "recurrenceRelation" ⓘ |
| Bernoulli polynomials | B_n(x+1) - B_n(x) = n x^{n-1} via predicate surface "recurrenceRelation" ⓘ |
| Bernoulli polynomials | B_n(x) = Σ_{k=0}^n {n \\ k} B_k x^{n-k} with suitable coefficients via predicate surface "recurrenceRelation" ⓘ |
| Catalan numbers | C_0 = 1 via predicate surface "recurrenceRelation" ⓘ |
| Catalan numbers | C_{n+1} = sum_{i=0}^{n} C_i C_{n-i} via predicate surface "recurrenceRelation" ⓘ |
| Catalan numbers | C_{n+1} = (4n+2)/(n+2) * C_n via predicate surface "recurrenceRelation" ⓘ |
| Bell numbers | B_{n+1} = \sum_{k=0}^{n} \binom{n}{k} B_k via predicate surface "recurrenceRelation" ⓘ |
| Bell numbers | B_n = \sum_{k=0}^{n} S(n,k) via predicate surface "recurrenceRelation" ⓘ |
| Bell numbers | B_{n} = \sum_{k=1}^{n} \binom{n-1}{k-1} B_{n-k} via predicate surface "recurrenceRelation" ⓘ |
| Gegenbauer polynomials | (n+1)C_{n+1}^{(\lambda)}(x) = 2(n+\lambda)x C_n^{(\lambda)}(x) - (n+2\lambda-1)C_{n-1}^{(\lambda)}(x) via predicate surface "recurrenceRelation" ⓘ |