Proof step e-5de7e20fcf013a10

basis_map A013609 → concludes about basis_map_A013609 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": "A013609",
  "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 b5f45866730096749ad3a4be3423b0c1fa08991760c66de0a3aee07286789631, 11,350 bytes (2,076 compressed); download JSON

Cited by

• n-25320566a4c11a38 (real_rooted)
• n-25320566a4c11a38 (one_signed_coefficients)
• n-25320566a4c11a38 (hadamard_kernel)