Proof step e-c19dc1e19e56bc04

basis_map A013611 → concludes about 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": "A013611",
  "operation": "basis_map"
}

Premises

• a(n) = 1 if n is of the form m(m+3)/2, otherwise 0. (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 c59809dd7bca09016a6f857e4c4c9cd7a84f04eccac157ee8efd93062ac14e10, 6,855 bytes (1,384 compressed); download JSON

Cited by

• n-2e0409c0014ec240 (one_signed_coefficients)
• n-2e0409c0014ec240 (hadamard_kernel)
• n-2e0409c0014ec240 (real_rooted)