Proof step e-1d35ea8dc489f8c6

basis_map A008288 → concludes about basis_map_A008288 of Triangle of coefficients in expansion of (1+4x)^n. JSON

Theorem

Affine-current basis map theorem polytool RealRooted orderTwoConstants_nonneg_iff ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A008288",
  "operation": "basis_map"
}

Premises

• Triangle of coefficients in expansion of (1+4x)^n. (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in [-1, 0]

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "lower": { "closed": true, "value": "-1564556493/268435456" }, "upper": { "closed": true, "value": "-46056243/268435456" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 3fc30af44c142ded7401fca42b413e8825f668aa38474b955347342b024fc3bd, 14,358 bytes (2,254 compressed); download JSON

Cited by

• n-215b7d121fbc1e4b (real_rooted)
• n-215b7d121fbc1e4b (one_signed_coefficients)
• n-215b7d121fbc1e4b (hadamard_kernel)