113250.lean`

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Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

7 declarations, 1 contain sorry, 0 declared as axioms

Expansion of g.f. $-(1 - 48x^2 - 256x^3) / ((1 - 4x)(1 + 4x)(1 + 4x + 16x^2))$

Corresponds to m = 4 in a family of 4th-order linear recurrence sequences

This sequence is defined by the linear recurrence relation with signature $(-4, 0, 64, 256)$ and initial values $a(0) = -1, a(1) = 4, a(2) = 32, a(3) = 64$. The recurrence is $a(n) = -4 a(n-1) + 64 a(n-3) + 256 a(n-4)$.

References:

A113250

Imports (1)

FormalConjecturesUtil

def OeisA113250.a a n is the sequence defined by the linear recurrence $a(n) = -4 a(n-1) + 64 a(n-3) + 256 a(n-4)$ with initial values $-1, 4, 32, 64$ line 39 source
Source documentation
a n is the sequence defined by the linear recurrence $a(n) = -4 a(n-1) + 64 a(n-3) + 256 a(n-4)$ with initial values $-1, 4, 32, 64$.

no axioms what this means
Statement uses: Nat, Int
2 instances, coercions and auxiliary constants left out.
```
def a : ℕ → ℤ
| 0 => -1
| 1 => 4
| 2 => 32
| 3 => 64
| n + 4 => -4 * a (n + 3) + 64 * a (n + 1) + 256 * a n

@[category test, AMS 11]
```
Mentions: test, AMS
theorem OeisA113250.a_0 line 47 source
no axioms what this means
Statement uses: Eq, Int, OeisA113250.a, OfNat.ofNat, Nat, Neg.neg
Proof uses: Eq.refl
4 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA113250.a_1 line 50 source
no axioms what this means
Statement uses: Eq, Int, OeisA113250.a, OfNat.ofNat, Nat
Proof uses: Eq.refl
3 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA113250.a_2 line 53 source
no axioms what this means
Statement uses: Eq, Int, OeisA113250.a, OfNat.ofNat, Nat
Proof uses: Eq.refl
3 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA113250.a_3 line 56 source
no axioms what this means
Statement uses: Eq, Int, OeisA113250.a, OfNat.ofNat, Nat
Proof uses: Eq.refl
3 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA113250.a_4 line 59 source
no axioms what this means
Statement uses: Eq, Int, OeisA113250.a, OfNat.ofNat, Nat, Neg.neg
Proof uses: Eq.refl
4 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA113250.conjecture sorry line 68 source
depends on sorry what this means
Statement uses: Nat, IsSquare, Int, OeisA113250.a, HAdd.hAdd, HMul.hMul, OfNat.ofNat
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
12 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.