Real-rooted atlas

Proof step

Geometric basis map (elementary)

Image under a basis map u^k -> P_k A013610

Concludes
basis_map_A013609 of Triangle T(n,k) = T(n-1,k) + 3*T(n-2,k-1) for k = 0..floor(n/2), with T(0,0) = 1, T(n,k) = 0 for n or k < 0, read by rows.
Premises
Theorem
polytool ?
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-33165e49bd0f30d2 · JSON
Operation
Image under a basis map u^k -> P_k
{
  "map": "A013610",
  "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 fbeeb3b690d398ba03ccd3821e2ae78b90bd46d92b113b7055c2d524afa81ded, 14,967 bytes (3,006 compressed); download
polytool replayed the certificate when the step was written.
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