Real-rooted atlas

Proof step

Geometric basis map (elementary)

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

Concludes
basis_map_A007318 of Triangle read by rows: T(n, k) = binomial(n, k) if n < 3, otherwise T(n, k) = binomial(n, k) + 2*binomial(n-2, k-1).
Premises
Theorem
polytool ?
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-72dddb5f81e709cd · 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": 4,
  "kind": "weak",
  "orientation": "unordered"
}
Certificate
basis_map, SHA-256 603614fbaed526022f5630dc6a8f5328faa2f961e34278849f4049cca6027c8f, 10,825 bytes (2,360 compressed); download
polytool replayed the certificate when the step was written.
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