Journal of Integer Sequences, Vol. 18 (2015), Article 15.5.7

A Generalization of the Digital Binomial Theorem

Hieu D. Nguyen
Department of Mathematics
Rowan University
Glassboro, NJ 08028


We prove a generalization of the digital binomial theorem by constructing a one-parameter subgroup of generalized Sierpiński matrices. In addition, we derive new formulas for the coefficients of Prouhet-Thue-Morse polynomials and describe group relations satisfied by generating matrices defined in terms of these Sierpiński matrices.

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(Concerned with sequence A010060.)

Received February 1 2015; revised version received April 30 2015. Published in Journal of Integer Sequences, May 26 2015.

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