Proof step e-f5362ff16cbef54d

basis_map A013610 → concludes about basis_map_A013610 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": "A013610",
  "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 cef6f78151cdd7ad7d3f3dfd03b22bbd58144cd37e82f8811d1b343307b6c337, 7,025 bytes (1,434 compressed); download JSON

Cited by

• n-0d95f7d056b9311c (real_rooted)
• n-0d95f7d056b9311c (one_signed_coefficients)
• n-0d95f7d056b9311c (hadamard_kernel)