Proof step e-1e942afebbc1521d

basis_map A008288 → concludes about basis_map_A008288 of Triangle of coefficients in expansion of (1+3*x)^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+3*x)^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, "exact": { "radicand": "2", "rational_part": "-3", "sqrt_coefficient": "-2" }, "value": "-1564556493/268435456" }, "upper": { "closed": true, "exact": { "radicand": "2", "rational_part": "-3", "sqrt_coefficient": "2" }, "value": "-46056243/268435456" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 f2010371820cc660dcc2e44472c83ebfd9e772ef86aaf961713699f0aa8e9353, 14,495 bytes (2,269 compressed); download JSON

Cited by

• n-bd22381760780feb (one_signed_coefficients)
• n-bd22381760780feb (hadamard_kernel)
• n-bd22381760780feb (real_rooted)