Real-rooted atlas

Proof step

Geometric basis map (elementary)

Image under a basis map u^k -> P_k A013611

Concludes
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…
Premises
Theorem
polytool ?
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-e2835d08a893163f · JSON
Operation
Image under a basis map u^k -> P_k
{
  "map": "A013611",
  "operation": "basis_map"
}
Claims
{
  "claim": "real_rooted",
  "from_index": 0,
  "region": {
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}
{
  "claim": "interlacing",
  "from_index": 1,
  "kind": "weak",
  "orientation": "unordered"
}
Certificate
basis_map, SHA-256 00db53a73b91097155a5c929324ab9ddcb1e275e54cad2e0291cbb01e6cd2e09, 14,828 bytes (2,978 compressed); download
polytool replayed the certificate when the step was written.
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