Real-rooted atlas

Proof step

Geometric basis map (elementary)

Image under a basis map u^k -> P_k A007318

Concludes
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 (0 <= k <= floor(n/2)…
Premises
Theorem
polytool ?
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-f9a40805442a5c9d · JSON
Operation
Image under a basis map u^k -> P_k
{
  "map": "A007318",
  "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 662d9653e5363ff219b9d4e87da545659e0a509ab0a2562465d993d60720a9c1, 10,829 bytes (2,442 compressed); download
polytool replayed the certificate when the step was written.
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