Proof step e-2a4594def0262eef

theorem_check three_term_recurrence → concludes about Triangle read by rows: T(n,k) number of tilings of a 2n X 3 grid by dominoes, 2k of which are in a vertical position (0<=k<=n). JSON

Theorem

Three-term recurrence criterion [Sze39, §3.3; Fav35] polytool ?

Operation

Theorem check of the node's own rule

{
  "operation": "theorem_check",
  "theorem": "three_term_recurrence"
}

Premises

None: this step is a direct theorem check.

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "lower": { "closed": false, "value": "-2" }, "upper": { "closed": false, "value": "0" } } }
• { "claim": "interlacing", "from_index": 1, "kind": "strict", "orientation": "previous_interlaces_next" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: theorem_check, SHA-256 7e1e5d7adf1401897d9ce1955b2cbb04f6e112340100c41b1634edcaed6fe0c4, 4,322 bytes (1,294 compressed); download JSON

Cited by

• n-8eb9bb3a09f0b7fd (one_signed_coefficients)
• n-8eb9bb3a09f0b7fd (hadamard_kernel)
• n-8eb9bb3a09f0b7fd (real_rooted)
• n-8eb9bb3a09f0b7fd (interlacing)

References

1. [Fav35] Jean Favard. Sur les polynômes de tchebicheff. C. R. Acad. Sci. Paris, 200:2052–2053, 1935.
2. [Sze39] G. Szegő. Orthogonal Polynomials. Colloquium publications, American Mathematical Society, 1939. doi:10.1090/coll/023