Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already declare readOnly/idempotent/non-destructive, so the bar is lower, and the description adds genuine context beyond them: a per-call price of $0.001 USDC via x402 on Solana, an equivalent HTTPS endpoint, and the output-encoding rule that terms past 15 digits become decimal strings. It stops short of describing the payment handshake or failure/refund behavior for a paid call.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

The recurrence definition is front-loaded in the first sentence and each following sentence carries distinct information (output mapping, domain, encoding rule, price, alternate endpoint). Slightly dense but no filler.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

With no output schema and no return-value annotations, the description supplies the output mapping and the decimal-string rule, which is the essential gap-filler. Left implicit are the exact response container (keys left/mid/right?) and the x402 payment flow, which for a paid tool would be worth a line.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema coverage is 0%, so the description must carry the parameter burden, and it does explain that n is the sequence index with a 3..4096 domain. However, that domain merely restates the schema's minimum/maximum and it never states the seed values T(0), T(1), T(2), which materially affect results.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific mathematical operation with the exact recurrence and names the three output components (left=T(n-3), mid=T(n-2), right=T(n-1)), which lets an agent predict the return shape. It does not distinguish itself from siblings such as tribonacci, trib_sum, trib_index, or trib_mod, so an agent cannot tell from the text alone which of those to pick.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

No when-to-use or when-not-to-use guidance is offered, and none of the abundant near-neighbor siblings (tribonacci, trib_sum, trib_mod, trib_index) are mentioned as alternatives. The only usage-relevant facts given are the domain of n and the payment model.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.