Proof step e-98125ea59568ff18

basis_map A007318 → concludes about basis_map_A007318 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": "A007318",
  "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 8c19ad51d6101a3cc4c1b2c9fa1f0ce30a531672b78acbe12ddbf622692e4a3c, 6,895 bytes (1,398 compressed); download JSON

Cited by

• n-39578f69b35e8349 (real_rooted)
• n-39578f69b35e8349 (one_signed_coefficients)
• n-39578f69b35e8349 (hadamard_kernel)