satisfiesRecurrence
P25791
predicate
Indicates that one entity fulfills or conforms to a specified recurrence relation defined by another entity.
All labels observed (4)
| Label | Occurrences |
|---|---|
| satisfiesRecurrence canonical | 6 |
| definedByRecurrence | 4 |
| recurrenceRule | 2 |
| satisfyRecurrence | 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: satisfiesRecurrence
Generated description
Indicates that one entity fulfills or conforms to a specified recurrence relation defined by another entity.
Sample triples (13)
| Subject | Object |
|---|---|
| Pascal's triangle | C(n,k) = C(n-1,k-1) + C(n-1,k) ⓘ |
| Fibonacci sequence | F(n) = F(n−1) + F(n−2) via predicate surface "definedByRecurrence" ⓘ |
| Ulam sequence | Each subsequent term is the smallest integer that can be written uniquely as the sum of two distinct earlier terms via predicate surface "definedByRecurrence" ⓘ |
| Knuth’s up-arrow notation | a ↑^n 1 = a for n ≥ 1 via predicate surface "recurrenceRule" ⓘ |
| Knuth’s up-arrow notation | a ↑^n (b+1) = a ↑^{n-1} (a ↑^n b) for n ≥ 2, b ≥ 1 via predicate surface "recurrenceRule" ⓘ |
| Gamma function | Γ(z+1)=zΓ(z) ⓘ |
| Sylvester sequence | a_1 = 2 via predicate surface "definedByRecurrence" ⓘ |
| Sylvester sequence | a_{n+1} = 1 + a_1 a_2 \cdots a_n via predicate surface "definedByRecurrence" ⓘ |
| Legendre polynomials | (n+1)P_{n+1}(x) = (2n+1)xP_n(x) - nP_{n-1}(x) via predicate surface "satisfyRecurrence" ⓘ |
| Chebyshev polynomials of the first kind | T_0(x) = 1 ⓘ |
| Chebyshev polynomials of the first kind | T_1(x) = x ⓘ |
| Chebyshev polynomials of the first kind | T_{n+1}(x) = 2x T_n(x) - T_{n-1}(x) ⓘ |
| Barnes G-function | G(n+1)=Γ(n)G(n) for positive integers n ⓘ |