Proof step e-6e2f4b29fae24343

basis_map A063967 → concludes about 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

Affine-current basis map theorem polytool RealRooted orderTwoConstants_nonneg_iff ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A063967",
  "operation": "basis_map"
}

Premises

• basis-map coefficients of Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downward antidiagonals. (sequence)
  uses: Every row P_n, n >= 1, is zero or real-rooted with all roots in [0, 0]

Claims

• { "claim": "real_rooted", "from_index": 1, "region": { "lower": { "closed": true, "value": "-5" }, "upper": { "closed": true, "value": "-1" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 bf805fe06274c52493a2450b4f5afd38d9eb2da7a2c23573961717174b75ceea, 13,492 bytes (2,084 compressed); download JSON

Cited by

• n-c72653d9ab0ee8be (real_rooted)
• n-c72653d9ab0ee8be (one_signed_coefficients)
• n-c72653d9ab0ee8be (hadamard_kernel)