Proof step e-1ebadae00ef5f3ca

basis_map A013609 → concludes about basis_map_A013609 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. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013609",
  "operation": "basis_map"
}

Premises

• 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, 0]

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 e981b94a84fd8f65026ca336547c72ef58d7b808ce95abea0c9e3466948ee367, 12,047 bytes (2,301 compressed); download JSON

Cited by

• n-726f071d833f296a (real_rooted)
• n-726f071d833f296a (one_signed_coefficients)
• n-726f071d833f296a (hadamard_kernel)