Proof step e-b77c7252fe4ee4d8

basis_map A008288 → concludes about basis_map_A008288 of 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

Affine-current basis map theorem polytool RealRooted orderTwoConstants_nonneg_iff ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A008288",
  "operation": "basis_map"
}

Premises

• 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). (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in [-2, 0]

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "lower": { "closed": true, "value": "-1564556493/268435456" }, "upper": { "closed": true, "value": "-46056243/268435456" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 9f856f5e954bf6d248563ecc61bd49d16783c63bba66c02ce02d75bad31f8e0b, 23,395 bytes (3,030 compressed); download JSON

Cited by

• n-1c7cd5e31010a2aa (real_rooted)
• n-1c7cd5e31010a2aa (one_signed_coefficients)
• n-1c7cd5e31010a2aa (hadamard_kernel)