Proof step e-8866dbf598c953fc

basis_map A013609 → concludes about basis_map_A013609 of The truncated (4,4,1)-Pascal triangle, given by 4*C(n-2, k) + 4*C(n-2, k-1) + C(n-2, k-2) for n>=2. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• The truncated (4,4,1)-Pascal triangle, given by 4*C(n-2, k) + 4*C(n-2, k-1) + C(n-2, k-2) for n>=2. (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 b5bda7912ae22be960137142411e020e4db4df80c2e3c56b2766d0f6a9cdb4f1, 6,897 bytes (1,404 compressed); download JSON

Cited by

• n-2fe6a26f73f75da6 (real_rooted)
• n-2fe6a26f73f75da6 (one_signed_coefficients)
• n-2fe6a26f73f75da6 (hadamard_kernel)