Proof step e-1a1a6d136d357a71

basis_map A013610 → concludes about basis_map_A013609 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

• Triangle whose (i,j)-th entry is binomial(i,j)*2^i. (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 0ee23918e2399a6cd2035fe5d52fff570fb514f13ddb44af7196af9047dd2365, 6,855 bytes (1,393 compressed); download JSON

Cited by

• n-4f34a2344b135a41 (real_rooted)
• n-4f34a2344b135a41 (one_signed_coefficients)
• n-4f34a2344b135a41 (hadamard_kernel)