Proof step e-f41ab3c7deb8e5d8

basis_map A007318 → concludes about basis_map_A007318 of Triangle read by rows: T(n,k) is the number of ternary words of length n having degree of asymmetry equal to k (n>=0; 0<=k<=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

• Triangle read by rows: T(n,k) is the number of ternary words of length n having degree of asymmetry equal to k (n>=0; 0<=k<=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 396af2a2c891ea7898c6a968e268161f159f29ef8367438cc2c86d6405c332a0, 6,885 bytes (1,398 compressed); download JSON

Cited by

• n-1a86492085c1e21c (one_signed_coefficients)
• n-1a86492085c1e21c (hadamard_kernel)
• n-1a86492085c1e21c (real_rooted)