Proof step e-52226b414d15e69f

basis_map A013610 → concludes about basis_map_A013610 of Triangle read by rows, T(n,k) = T(n-1,k) + T(n-2,k) + T(n-1,k-1) + T(n-2,k-1) and T(0,0) = 1. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Triangle read by rows, T(n,k) = T(n-1,k) + T(n-2,k) + T(n-1,k-1) + T(n-2,k-1) and T(0,0) = 1. (sequence)
  uses: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 1, "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 d1e89ac5a04d46552f57db40d821d536c1364723242db09422894e2c6161d0dc, 12,047 bytes (2,300 compressed); download JSON

Cited by

• n-51fcbaaf07b9691b (real_rooted)
• n-51fcbaaf07b9691b (one_signed_coefficients)
• n-51fcbaaf07b9691b (hadamard_kernel)