Real-rooted atlas

Proof step

Geometric basis map (elementary)

Image under a basis map u^k -> P_k A013609

Concludes
basis_map_A013609 of Triangle read by rows: T(n,k) number of tilings of a 2n X 3 grid by dominoes, 2k of which are in a vertical position (0<=k<=n).
Premises
Theorem
polytool ?
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-15998779e1d02171 · JSON
Operation
Image under a basis map u^k -> P_k
{
  "map": "A013609",
  "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 dbcf2be948d55ec3630d345f10c03124f1527bf542f23828489a31a27b83cbc7, 13,584 bytes (2,590 compressed); download
polytool replayed the certificate when the step was written.
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