Proof step e-f5eca334b4637498

preserver_image affine, 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): Polynomial.Splits.comp_of_degree_le_one

Operation

Image under a real-rootedness preserver

{
  "index_shift": 0,
  "operation": "preserver_image",
  "operator": "{\"shape\":\"affine\",\"slope\":\"1\",\"intercept\":\"1\"}"
}

Premises

• a(n) = 1 if n is a triangular number, otherwise 0. (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Claims

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

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: preserver_image, SHA-256 4a06f3df78802774a252086980dde93b3c28c7ab18e1ec926ec24e79e07eeaa4, 4,726 bytes (1,462 compressed); download JSON

Cited by

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