Proof step e-fca58ee161653196

basis_map A008288 → concludes about basis_map_A008288 of Triangular array read by rows. T(n, k) is the coefficient of x^k in a(n+3) where a(1) = a(2) = a(3) = 1 and a(m+2) = (m*x + 2)*a(m+1) - a(… 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

• Triangular array read by rows. T(n, k) is the coefficient of x^k in a(n+3) where a(1) = a(2) = a(3) = 1 and a(m+2) = (m*x + 2)*a(m+1) - a(m… (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in [-2, 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 ab071cd420dc37d5df449d8c8c3041c916d8ab89392fb98a15abe19665f7c874, 23,804 bytes (3,105 compressed); download JSON

Cited by

• n-ee5b69bc1fbff350 (hadamard_kernel)
• n-ee5b69bc1fbff350 (real_rooted)
• n-ee5b69bc1fbff350 (one_signed_coefficients)