Theorems · Theorem · combinatorics
Nat.sum_range_choose_sq
∀ (n : ℕ), ∑ i ∈ Finset.range (n + 1), n.choose i ^ 2 = (2 * n).choose n
The sum of entries squared in a row of Pascal's triangle
- Defined in
- Mathlib.Data.Nat.Choose.Vandermonde
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finset.sumstatement and proof · cited by 5,195
- Finset.sum_congrproof · cited by 2,323
- Finset.rangestatement and proof · cited by 1,341
- Nat.choosestatement and proof · cited by 494
- sqproof · cited by 280
- two_mulproof · cited by 232
- Finset.mem_range_succ_iffproof · cited by 22
- Nat.choose_symmproof · cited by 15
- Finset.Nat.sum_antidiagonal_eq_sum_range_succ_mkproof · cited by 14
- Nat.add_choose_eqproof · cited by 2
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.