Proof step e-d4e342c4e7f76e08

basis_map A007318 → concludes about basis_map_A007318 of Triangle of Sulanke numbers: T(n,k) = T(n,k-1) + a(n-1,k) for n+k even and a(n,k) = a(n,k-1) + 2*a(n-1,k) for n+k odd. 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 Sulanke numbers: T(n,k) = T(n,k-1) + a(n-1,k) for n+k even and a(n,k) = a(n,k-1) + 2*a(n-1,k) for n+k odd. (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 99ee56fb59ae0b5fda23c86440ea734e6e5f957a3d62caed09424063d8c4f38d, 7,011 bytes (1,425 compressed); download JSON

Cited by

• n-73875e607efb6f6a (real_rooted)
• n-73875e607efb6f6a (one_signed_coefficients)
• n-73875e607efb6f6a (hadamard_kernel)