Proof step e-d33b5447346a6a36

basis_map A013610 → concludes about basis_map_A007318 of Triangle of coefficients in expansion of (1+3*x)^n. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013610",
  "operation": "basis_map"
}

Premises

• Cube of lower triangular normalized binomial matrix. (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 0425f87c188261f83e88e8f2f3087602619c83829ac026f9caefe0e683e0229b, 6,855 bytes (1,389 compressed); download JSON

Cited by

• n-e8c6285b75cf03a2 (real_rooted)
• n-e8c6285b75cf03a2 (one_signed_coefficients)
• n-e8c6285b75cf03a2 (hadamard_kernel)