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The for- mula to calculate the nth centered hexagonal number is given by:1+6+ 12 +...+ 6(n− 1), which simpli- fies to3n 2 −3n+

By substituting the sum of the first (n-1) natural numbers into the expression, we get ‘1 + 6*((n- 1)*n/2)‘, which simplifies to ‘1 + 3*n*(n-1)‘

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2026 1

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CONDITIONAL 1

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PPDL: LLM-Based Flows as Probabilistic Programs

cs.LG · 2026-08-05 · conditional · novelty 7.0

PPDL adds factor-based probabilistic inference to a prompt programming language, turning multi-step LLM flows into distributions over execution traces with pluggable inference engines.

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  • PPDL: LLM-Based Flows as Probabilistic Programs cs.LG · 2026-08-05 · conditional · none · ref 1

    PPDL adds factor-based probabilistic inference to a prompt programming language, turning multi-step LLM flows into distributions over execution traces with pluggable inference engines.