Real-rooted atlas

Proof step

Affine, reversal and Möbius substitutions (elementary)

Image under a real-rootedness preserver affine, shift 0

Concludes
Triangle T(n,k) = 3*T(n-1,k) + T(n-3,k-1) for k = 0..floor(n/3) with T(0,0) = 1 and T(n,k) = 0 for n or k < 0, read by rows.
Premises
Theorem
polytool ?
Lean
RealRooted Polynomial.Splits.comp_of_degree_le_one
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-a4aa4a63e33d8171 · JSON
Operation
Image under a real-rootedness preserver
{
  "index_shift": 0,
  "operation": "preserver_image",
  "operator": "{\"shape\":\"affine\",\"slope\":\"1/27\",\"intercept\":\"0\"}"
}
Claims
{
  "claim": "real_rooted",
  "from_index": 0,
  "region": {
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}
Certificate
preserver_image, SHA-256 4cf787d1320bdd672cd37b55206e811be112dad57d94041807c52ff760072f55, 7,530 bytes (2,274 compressed); download
polytool replayed the certificate when the step was written.
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