Proof step e-5dc8ce8b8b471ab9

basis_map A007318 → concludes about Bisection of Fibonacci triangle A037027: even-indexed members of column sequences of A037027 (not counting leading zeros). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Triangular array binomial(2*n-k, k), k=0..n, n >= 0. (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" } } }
• { "claim": "interlacing", "from_index": 1, "kind": "weak", "orientation": "unordered" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 975d7833ed1e38571d606d37688aa394827e6e075d1d116b6c5d0bea1b1a6c5c, 13,622 bytes (2,593 compressed); download JSON

Cited by

• n-fac4d4a000d744e8 (one_signed_coefficients)
• n-fac4d4a000d744e8 (hadamard_kernel)
• n-fac4d4a000d744e8 (interlacing)
• n-fac4d4a000d744e8 (real_rooted)