Proof step e-a0d290e16ed9f688

basis_map A013609 → concludes about basis_map_A007318 of Triangle of coefficients in expansion of (1+4x)^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 whose (i,j)-th entry is binomial(i,j)*3^(i-j)*2^j. (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 c9a4c83c05c10461e1a76db9fb6df0a9d70ad2ce1f801de4b259f526ce91964d, 6,855 bytes (1,391 compressed); download JSON

Cited by

• n-d04994959b21388c (real_rooted)
• n-d04994959b21388c (one_signed_coefficients)
• n-d04994959b21388c (hadamard_kernel)