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) is the number of ternary words of length n having k runs of consecutive 0's (0<=k<=ceiling(n/2)).
Premises
Theorem
polytool ?
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-9163e74e00c6af70 · 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": 1,
  "kind": "weak",
  "orientation": "unordered"
}
Certificate
basis_map, SHA-256 5a2d8c98f7717ab2d4a794106465164dc6ec19c46b8cc8334b24c8f797883cc0, 14,407 bytes (2,853 compressed); download
polytool replayed the certificate when the step was written.
Cited by