Proof step e-6e97878f95ac8f6d

basis_map A007318 → concludes about basis_map_A007318 of Triangle, read by rows of 2*n+1 terms, where row n lists the coefficients in (1+3*x+2*x^2)^n. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Triangle, read by rows of 2*n+1 terms, where row n lists the coefficients in (1+3*x+2*x^2)^n. (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 9dabed1e414629b3248436610865199ee46c4b1d58262d166cc6e707b424663d, 6,875 bytes (1,390 compressed); download JSON

Cited by

• n-a19ad5e2037d7c6a (real_rooted)
• n-a19ad5e2037d7c6a (one_signed_coefficients)
• n-a19ad5e2037d7c6a (hadamard_kernel)