112521.lean`

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

9 declarations, 1 contain sorry, 0 declared as axioms

Sequence related to NOR bracketings

$$a(n) = \sum_{j=0}^{n-1} (-1)^j \binom{2j}{j} \binom{2n-j-2}{n-j-1}$$

References:

A112521

Imports (1)

FormalConjecturesUtil

def OeisA112521.a a n is the $n$-th term of the sequence related to NOR bracketings line 38 source
Source documentation
a n is the $n$-th term of the sequence related to NOR bracketings.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: Int.toNat, Finset.sum, Int, Finset.range, Nat.choose, HMul.hMul, OfNat.ofNat, HSub.hSub, HAdd.hAdd, ite, Eq, HMod.hMod, Neg.neg
15 instances, coercions and auxiliary constants left out.
```
def a (n : ℕ) : ℕ :=
…
```
theorem OeisA112521.a_0 line 50 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA112521.a, OfNat.ofNat
Proof uses: of_decide_eq_true, id, Bool, Decidable.decide, Bool.true, 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 OeisA112521.a_1 line 53 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA112521.a, OfNat.ofNat
Proof uses: of_decide_eq_true, id, Bool, Decidable.decide, Bool.true, 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 OeisA112521.a_2 line 56 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA112521.a, OfNat.ofNat
Proof uses: of_decide_eq_true, id, Bool, Decidable.decide, Bool.true, 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 OeisA112521.a_3 line 59 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA112521.a, OfNat.ofNat
Proof uses: of_decide_eq_true, id, Bool, Decidable.decide, Bool.true, 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 OeisA112521.a_4 line 62 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA112521.a, OfNat.ofNat
Proof uses: of_decide_eq_true, id, Bool, Decidable.decide, Bool.true, 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 OeisA112521.a_5 line 65 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA112521.a, OfNat.ofNat
Proof uses: of_decide_eq_true, id, Bool, Decidable.decide, Bool.true, Eq.refl
3 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
def OeisA112521.T T n k is the array defined as $T(1,1) = 1$, $T(i,j) = 0$ if $i<1$ or $j<1$, $T(n,k) = T(n,k-2) + T(n,k-1) - 2 T(n-1,k-1) + T(n-1,k) + T(n-2,k)$ line 71 source
Source documentation
T n k is the array defined as $T(1,1) = 1$, $T(i,j) = 0$ if $i<1$ or $j<1$, $T(n,k) = T(n,k-2) + T(n,k-1) - 2 T(n-1,k-1) + T(n-1,k) + T(n-2,k)$.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat, Int
Proof uses: PSigma.mk
1 instances, coercions and auxiliary constants left out.
```
def T (n k : ℕ) : ℤ :=
…
```
theorem OeisA112521.conjecture sorry line 84 source
depends on sorry what this means
Statement uses: Nat, GE.ge, OfNat.ofNat, Eq, Int, OeisA112521.a, OeisA112521.T
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
8 instances, coercions and auxiliary constants left out.

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