Proof step e-f721257c9beb3a40

basis_map A013610 → concludes about basis_map_A013610 of Triangle read by rows: T(n,k) is the number of ways to tile a 2 X n rectangle with k pieces of 2 X 2 tiles and n-2k pieces of 1 X 2 tiles … JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013610",
  "operation": "basis_map"
}

Premises

• Triangle read by rows: T(n,k) is the number of ways to tile a 2 X n rectangle with k pieces of 2 X 2 tiles and n-2k pieces of 1 X 2 tiles (… (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 20b94261ba7e4274c62d88e834c6de97a07bbede25e04173da87e3004028b6d2, 12,071 bytes (2,381 compressed); download JSON

Cited by

• n-b5ebaf3676d81658 (real_rooted)
• n-b5ebaf3676d81658 (one_signed_coefficients)
• n-b5ebaf3676d81658 (hadamard_kernel)