Proof step e-64a82ef46e481e9c

basis_map A013609 → concludes about basis_map_A013609 of Triangle of coefficients in expansion of (1+6x)^n. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Triangle of coefficients in expansion of (1+6x)^n. (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 afd5c793f213179d4f2f7f40ab91652b4feda0e28fd62e2560293714c56ff68e, 6,857 bytes (1,389 compressed); download JSON

Cited by

• n-96d5ef3a0d05e14f (real_rooted)
• n-96d5ef3a0d05e14f (one_signed_coefficients)
• n-96d5ef3a0d05e14f (hadamard_kernel)