Proof step e-01e7c46c78122cbc

basis_map A007318 → concludes about Triangle whose (i,j)-th entry is binomial(i,j)*3^(i-j)*2^j. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Triangle of coefficients in expansion of (1+2*x)^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 16955e1cb3946de9b0e2afee079bf505c80eeab8e42d893e1e68a5f1b04f2b5f, 6,855 bytes (1,385 compressed); download JSON

Cited by

• n-01cea33b6485d9cc (one_signed_coefficients)
• n-01cea33b6485d9cc (hadamard_kernel)
• n-01cea33b6485d9cc (real_rooted)