Proof step e-5c9cfcdf7ca38f64

basis_map A013611 → concludes about basis_map_A013611 of Triangle T(n,k) = 3*T(n-1,k) + T(n-3,k-1) for k = 0..floor(n/3) with T(0,0) = 1 and T(n,k) = 0 for n or k < 0, read by rows. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013611",
  "operation": "basis_map"
}

Premises

• Triangle T(n,k) = 3*T(n-1,k) + T(n-3,k-1) for k = 0..floor(n/3) with T(0,0) = 1 and T(n,k) = 0 for n or k < 0, read by rows. (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" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 b01ffe19c41fd66ea558fa5fa69d602c5576024ace310b54c86979118827927a, 11,350 bytes (2,073 compressed); download JSON

Cited by

• n-11f6a813858a42ee (one_signed_coefficients)
• n-11f6a813858a42ee (hadamard_kernel)
• n-11f6a813858a42ee (real_rooted)