Proof step e-99f76b7466efc63d

basis_map A007318 → concludes about a(n) = 1 if n is a triangular number, otherwise 0. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A007318",
  "operation": "basis_map"
}

Premises

• a(n) = 1 if n is a triangular number, 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 6730028f302905adce04b646e5a9f4b72a9bf1a3bacb2aa318042697705a3a3c, 6,835 bytes (1,377 compressed); download JSON

Cited by

• n-39194b37db596ae8 (real_rooted)
• n-39194b37db596ae8 (one_signed_coefficients)
• n-39194b37db596ae8 (hadamard_kernel)