Proof step e-4aa3bf1829d77c70

basis_map A013609 → concludes about shift_x_plus_one of Triangle read by rows: T(n,k) is the number of ways to tile a 3 X n rectangle with k pieces of 2 X 2 tiles and 3n-4k pieces of 1 X 1 tiles … JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013609",
  "operation": "basis_map"
}

Premises

• Triangle read by rows: T(n,k) is the number of ways to tile a 2 X n rectangle with k pieces of 2 X 2 tiles and n-2k pieces of 1 X 2 tiles (… (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" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 2ad45a1518a938d923bccf0bec418b8949c30f13ad86660269554f98eea5c4cc, 12,071 bytes (2,382 compressed); download JSON

Cited by

• n-0d89b6177f6a1dbb (one_signed_coefficients)
• n-0d89b6177f6a1dbb (hadamard_kernel)
• n-0d89b6177f6a1dbb (real_rooted)