Proof step e-37edf5cceba94f47

basis_map A038327 → concludes about Triangle read by rows, T(n,k) = T(n-1,k) + T(n-2,k) + T(n-1,k-1) + T(n-2,k-1) and T(0,0) = 1. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A038327",
  "operation": "basis_map"
}

Premises

• basis-map coefficients of Triangle read by rows, T(n,k) = T(n-1,k) + T(n-2,k) + T(n-1,k-1) + T(n-2,k-1) and T(0,0) = 1. (sequence)
  uses: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 12]

Claims

• { "claim": "real_rooted", "from_index": 1, "region": { "upper": { "closed": true, "value": "0" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 ed2ed6a297e8a94af1b8c92494baa9f8bec2cd17d1f5bc0137f5e864755d9ce1, 12,089 bytes (2,309 compressed); download JSON

Cited by

• n-c72653d9ab0ee8be (one_signed_coefficients)
• n-c72653d9ab0ee8be (hadamard_kernel)
• n-c72653d9ab0ee8be (real_rooted)