Proof step e-3d28f25fd9699ebd

basis_map A013611 → concludes about basis_map_A013611 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": "A013611",
  "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 e6b146699de615058aa1940dfe3e6a987697bc2acebbf61eb02efec55a6393ba, 6,899 bytes (1,403 compressed); download JSON

Cited by

• n-d021e887e4fd1eea (real_rooted)
• n-d021e887e4fd1eea (one_signed_coefficients)
• n-d021e887e4fd1eea (hadamard_kernel)