Proof step e-3a20d12bade77e7f

basis_map A007318 → concludes about basis_map_A007318 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": "A007318",
  "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 6754dd78a64b1cf1c467fc50e5d4b603a4618b5d044ecf15199e5ca387ad9d87, 12,047 bytes (2,295 compressed); download JSON

Cited by

• n-c63944481deaae45 (real_rooted)
• n-c63944481deaae45 (one_signed_coefficients)
• n-c63944481deaae45 (hadamard_kernel)