Proof step e-97db6227df9d6f92

basis_map A099093 → concludes about Riordan array (1, 3+3x). JSON

Theorem

Affine-current basis map theorem polytool RealRooted orderTwoConstants_nonneg_iff ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A099093",
  "operation": "basis_map"
}

Premises

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

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "lower": { "closed": true, "value": "-4/3" }, "upper": { "closed": true, "value": "0" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 ae21c3aab0072bcb0b759810d40fcc82ed63fe0f50d34afa198133f91513d59a, 13,507 bytes (2,070 compressed); download JSON

Cited by

• n-016d7724d51f6416 (real_rooted)
• n-016d7724d51f6416 (one_signed_coefficients)
• n-016d7724d51f6416 (hadamard_kernel)