Proof step e-260a6c47d63b7967

basis_map A013610 → concludes about basis_map_A013610 of Triangle read by rows: T(0,0) = 1; T(n,k) = T(n-1,k) + 3 * T(n-4,k-1) for k = 0..floor(n/4); T(n,k)=0 for n or k < 0. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013610",
  "operation": "basis_map"
}

Premises

• Triangle read by rows: T(0,0) = 1; T(n,k) = T(n-1,k) + 3 * T(n-4,k-1) for k = 0..floor(n/4); T(n,k)=0 for n or k < 0. (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "0" } } }
• { "claim": "interlacing", "from_index": 1, "kind": "weak", "orientation": "unordered" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 1eeb25dc1b8eea02fafed39eec6253dace023798a9bd3ce314754e086972652c, 10,756 bytes (2,414 compressed); download JSON

Cited by

• n-0eebbccc63cc701f (real_rooted)
• n-0eebbccc63cc701f (one_signed_coefficients)
• n-0eebbccc63cc701f (hadamard_kernel)
• n-0eebbccc63cc701f (interlacing)