Proof step e-be49b310b519d57a

basis_map A030528 → concludes about Triangle read by rows: T(n,k) = binomial(k,n-k). JSON

Theorem

Affine-current basis map theorem polytool RealRooted orderTwoConstants_nonneg_iff ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A030528",
  "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" }, "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 6552e64a50620355be026c2dafda9184fec3e73097a01da59d745b6784480a8b, 13,475 bytes (2,060 compressed); download JSON

Cited by

• n-21854f4257effb01 (one_signed_coefficients)
• n-21854f4257effb01 (hadamard_kernel)
• n-21854f4257effb01 (real_rooted)