113254.lean`

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

7 declarations, 1 contain sorry, 0 declared as axioms

Square odd-indexed terms in the recurrence $a(n) = 8a(n-1) - 8a(n-2) + 8a(n-3) - a(n-4)$

A113254: Corresponds to $m = 8$ in a family of 4th-order linear recurrence sequences.

The sequence $a(n)$ is defined by the initial conditions $a(0)=-1, a(1)=4, a(2)=176, a(3)=3136$, and the linear recurrence relation $a(n) = -4 * a (n-1) + 256 * a (n-3) + 4096 * a (n-4)$ for $n \ge 4$.

References:

A113254
arxiv/2605.22763 Advancing Mathematics Research with AI-Driven Formal Proof Search by George Tsoukalas et al.

Imports (1)

FormalConjecturesUtil

def OeisA113254.a Documented declaration: a line 46 source
Source documentation
The sequence $a(n)$ is defined by the initial conditions $a(0)=-1, a(1)=4, a(2)=176, a(3)=3136$, and the linear recurrence relation $a(n) = -4 * a (n-1) + 256 * a (n-3) + 4096 * a (n-4)$ for $n \ge 4$.

no axioms what this means
Statement uses: Nat, Int
2 instances, coercions and auxiliary constants left out.
```
def a (n : ℕ) : ℤ :=
…
```
lemma OeisA113254.a_0 line 56 source
no axioms what this means
Statement uses: Eq, Int, OeisA113254.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.
lemma OeisA113254.a_1 line 59 source
no axioms what this means
Statement uses: Eq, Int, OeisA113254.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.
lemma OeisA113254.a_2 line 62 source
no axioms what this means
Statement uses: Eq, Int, OeisA113254.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.
lemma OeisA113254.a_3 line 65 source
no axioms what this means
Statement uses: Eq, Int, OeisA113254.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.
lemma OeisA113254.a_4 line 68 source
no axioms what this means
Statement uses: Eq, Int, OeisA113254.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 OeisA113254.a_odd_is_square sorry line 79 source
depends on sorry what this means
Statement uses: Nat, IsSquare, Int, OeisA113254.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.