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Fungrim entry: acdce8

p(n)=∑k=1n+1(−1)k+1(p ⁣(n−k(3k−1)2)+p ⁣(n−k(3k+1)2))p(n) = \sum_{k=1}^{n + 1} {\left(-1\right)}^{k + 1} \left(p\!\left(n - \frac{k \left(3 k - 1\right)}{2}\right) + p\!\left(n - \frac{k \left(3 k + 1\right)}{2}\right)\right)
Assumptions:n∈Zn \in \mathbb{Z}
TeX:
p(n) = \sum_{k=1}^{n + 1} {\left(-1\right)}^{k + 1} \left(p\!\left(n - \frac{k \left(3 k - 1\right)}{2}\right) + p\!\left(n - \frac{k \left(3 k + 1\right)}{2}\right)\right)

n \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
PartitionsPp(n)p(n) Integer partition function
Sum∑nf(n)\sum_{n} f(n) Sum
Powab{a}^{b} Power
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("acdce8"),
    Formula(Equal(PartitionsP(n), Sum(Mul(Pow(-1, Add(k, 1)), Add(PartitionsP(Sub(n, Div(Mul(k, Sub(Mul(3, k), 1)), 2))), PartitionsP(Sub(n, Div(Mul(k, Add(Mul(3, k), 1)), 2))))), For(k, 1, Add(n, 1))))),
    Variables(n),
    Assumptions(Element(n, ZZ)))

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2021-03-15 19:12:00.328586 UTC