Proof step e-88f7d5697e008187

preserver_image reversal, shift 0 → concludes about a(n) = 1 if n is a triangular number, otherwise 0. JSON

Theorem

Affine, reversal and Möbius substitutions (elementary) polytool ?

Lean (RealRooted): route reversed RealRooted.X_pow_mul_reverse_eq_zero_or_splits, RealRooted.reflect_eq_zero_or_splits

Operation

Image under a real-rootedness preserver

{
  "index_shift": 0,
  "operation": "preserver_image",
  "operator": "{\"shape\":\"reversal\",\"schedule\":{\"first_index\":1,\"first_degree\":0,\"step\":1}}"
}

Premises

• basis-map coefficients of Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downward antidiagonals. (sequence)
  uses: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 1, "region": { "upper": { "closed": true, "value": "0" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: preserver_image, SHA-256 6684baf6eb242ec6dcadae746f201a75733132dc36f1ab9592ba1c167984bc8a, 5,017 bytes (1,542 compressed); download JSON

Cited by

• n-39194b37db596ae8 (real_rooted)
• n-39194b37db596ae8 (one_signed_coefficients)
• n-39194b37db596ae8 (hadamard_kernel)