Proof step e-28b777b3c0b25332

basis_map A013610 → concludes about basis_map_A013610 of Twice Pascal's triangle A007318: T(n,k) = 2*C(n,k). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Twice Pascal's triangle A007318: T(n,k) = 2*C(n,k). (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 416bf6eac3b56e94c126860aabfcef5dc7b1a6cf88bc186c7cf3dddf2c5fa319, 6,855 bytes (1,390 compressed); download JSON

Cited by

• n-0f5fb19aff15410b (real_rooted)
• n-0f5fb19aff15410b (one_signed_coefficients)
• n-0f5fb19aff15410b (hadamard_kernel)