Proof step e-b1356930ce9c898c

basis_map A013609 → concludes about basis_map_A013609 of Triangle T(n,k) = 3*T(n-1,k) + T(n-4,k-1) for k = 0..floor(n/4), with T(0,0) = 1 and T(n,k) = 0 for n or k < 0, read by rows. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013609",
  "operation": "basis_map"
}

Premises

• Triangle T(n,k) = 3*T(n-1,k) + T(n-4,k-1) for k = 0..floor(n/4), with T(0,0) = 1 and T(n,k) = 0 for n or k < 0, read by rows. (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": "0" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 eafaeee151d10ad009f7b26f4d58603cd597241f51d88437c4fe60011f73d3aa, 11,385 bytes (2,081 compressed); download JSON

Cited by

• n-84604e10f166b874 (one_signed_coefficients)
• n-84604e10f166b874 (hadamard_kernel)
• n-84604e10f166b874 (real_rooted)