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This research note presents a weighted matrix construction based on the parity pattern of Pascal's triangle modulo 2, represented by the Sierpiński Pascal matrix. By applying a binary carry characterization, the construction yields the sequence a(n) = (8n − 2n)/3, which coincides with the classical enumeration formula for monic irreducible cubic polynomials over GF(2n).
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Juan Camilo Hernández-Torres (2026) studied this question.
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