Proof step e-0985ee5bc77b64e0

basis_map A007318 → concludes about shift_x_plus_one of Square array of Delannoy numbers D(i,j) (i >= 0, j >= 0) read by antidiagonals. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Square array of Delannoy numbers D(i,j) (i >= 0, j >= 0) read by antidiagonals. (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" } } }
• { "claim": "interlacing", "from_index": 2, "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 5492e29ab1d5bd773023b0e7e95bf5ec0e6c565473717ff504a3cda091bbe028, 14,011 bytes (2,696 compressed); download JSON

Cited by

• n-85a14e0b559789f0 (one_signed_coefficients)
• n-85a14e0b559789f0 (hadamard_kernel)
• n-85a14e0b559789f0 (interlacing)
• n-85a14e0b559789f0 (real_rooted)