ScorpTech x402 API

Motzkin

motzkin

Read-onlyIdempotent

The nth Motzkin number. M0 and M1 are 1, M2 is 2, M4 is 9, from M_n = sum binom(n, 2k) C_k. n runs from 0 to 512. An optional modulus reduces the term; zero is rejected. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/motzkin

Tool call template

Replace each placeholder with a value matching the input schema. Only required parameters are included; add optional parameters as needed.

{
  "id": 1,
  "jsonrpc": "2.0",
  "method": "tools/call",
  "params": {
    "arguments": {
      "n": "<n>"
    },
    "name": "motzkin"
  }
}

Input Schema

Name	Required	Description	Default
`n`	Yes
`mod`	No

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A3.6/5.0

Behavior4/5

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

The description adds important behavior beyond the annotations: the n range 0–512, optional modulus behavior with zero rejected, cost of $0.001 USDC per successful call, and an alternate HTTPS endpoint. It does not describe the return format, but pricing and error behavior are transparent.

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

Conciseness5/5

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

The description is front-loaded with the core purpose, then efficiently adds base cases, range, modulus behavior, pricing, and endpoint in a compact passage. Every clause contributes useful information without waste.

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

Completeness4/5

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

For a simple pure-function tool with no output schema and rich annotations, the description covers the important call-time details: valid n range, optional modulus semantics, pricing, and alternate endpoint. It could state the return type more explicitly, but the mathematical definition makes it clear.

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

Parameters3/5

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

Schema description coverage is 0%, so the description must compensate. It documents n's range and the optional modulus's effect and rejection of zero, but it does not explain that mod is a decimal string up to 200 digits, leaving some schema-level detail unaddressed.

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

Purpose4/5

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

The description clearly identifies the tool as returning the nth Motzkin number, with base cases and a recurrence to disambiguate the sequence. It does not explicitly contrast with sibling sequence tools, but the resource is specific enough to be unambiguous.

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

Usage Guidelines2/5

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

No guidance is given on when to use this tool versus alternatives; the siblings include many other sequence tools but none are mentioned. The description only supplies parameter constraints, not usage context or exclusions.

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

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