Proof step e-51a31f555c517eab

basis_map A013611 → concludes about basis_map_A013609 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": "A013611",
  "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 cd5ee2a35724fc7df2ba7196ce4f26d3d265f4b341c5a89e3211736bc7bd20f2, 12,071 bytes (2,381 compressed); download JSON

Cited by

• n-9e53622e0c440ce5 (real_rooted)
• n-9e53622e0c440ce5 (one_signed_coefficients)
• n-9e53622e0c440ce5 (hadamard_kernel)