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) for n < 2 and binomial(n, k) + 3^(n-1)*binomial(n-2, k -1) otherwise.
Premises
Theorem
polytool ?
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-0bc3868d003d16cc · 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": 3,
  "kind": "weak",
  "orientation": "unordered"
}
Certificate
basis_map, SHA-256 771b5c4fd833e6ed16eeeb13bb941acd0c73c77b4e6a398ee524e48aa1ee4754, 16,457 bytes (3,228 compressed); download
polytool replayed the certificate when the step was written.
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