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) = binomial(n, k) for n < 2 and binomial(n, k) + 2^(n-1) * binomial(n-2, k-1) otherwise.
Premises
Theorem
polytool ?
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-289c399f4e1cc521 · 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": 3,
  "kind": "weak",
  "orientation": "unordered"
}
Certificate
basis_map, SHA-256 6b68965b91009629dc1a8f1b607204a2e5e6b8f6ec6b483a2d236eed60ac8fa9, 16,440 bytes (3,234 compressed); download
polytool replayed the certificate when the step was written.
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