Proof step

Geometric basis map (elementary)

Image under a basis map u^k -> P_k A013610

Concludes

Premises

theta_plus_one of a(n) = 1 if n is of the form m(m+3)/2, otherwise 0.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Theorem

polytool ?

Checked

polytool replayed · Lean not attempted

Technical details

Step id

e-62d29b6a8cc71779 · JSON

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013610",
  "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 5ad9af84c8703511a8bf70b6b68306c4f07d98174a7d47843ac89e249881ba0e, 14,742 bytes (2,742 compressed); download

polytool replayed the certificate when the step was written.

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