The Spiked Pascal Sequence: A Novel Algorithmic Variant and Its Applications

This paper introduces the "Spiked Pascal Sequence" (SPS), a novel algorithmic variant of Pascal's triangle that enforces specific uniqueness constraints and selective termination conditions within a dynamic array architecture. Standard binomial expansion produces linear/smooth growth, whereas SPS generates a non-smooth geometric phenomenon characterized by a stabilized mathematical plateau interrupted by a deterministic central spike scaling on the order of O(2^n). The paper details:1. The formal mathematical definition and step-back symmetry rules.2. An efficient C++ dynamic array/hash-set algorithmic implementation.3. Predictive closed-form modeling that allows O(1) time complexity computation of the central spike.4. Multidisciplinary applications across computer science (cryptography, zero-metadata network payload compression, image filtering) and physical sciences (heat dissipation, wave dynamics, traffic flow).