Proof step e-54652e8af65208a6

basis_map A008288 → concludes about a(n) = 1 if n is a triangular number, otherwise 0. 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

• a(n) = 1 if n is a triangular number, otherwise 0. (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in [-10368968295/4294967296, 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 8beeffdaabcce06fa4f99464a5d0726400e6c5cffc40d2213099741847f19119, 14,269 bytes (2,233 compressed); download JSON

Cited by

• n-39194b37db596ae8 (one_signed_coefficients)
• n-39194b37db596ae8 (hadamard_kernel)
• n-39194b37db596ae8 (real_rooted)