Concrete Math
Recurrent Construction of MacWilliams and Chebyshev Matrices
Fundamenta Informaticae - Words, Graphs, Automata, and Languages; Special Issue Honoring the 60th Birthday of Professor Tero Harju
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A relationship between the MacWilliams transform matrices and the classical integer Fibonacci, Lucas, and Padovan sequences is established. Namely, it is proved that the summation over some naturally chosen planes in the pyramid composed of these matrices yields a new integer sequence, which is the convolution of the Fibonacci numbers and the (alternating) Padovan numbers. In turn, this convolution is linearly represented in terms of the Lucas numbers and the Padovan numbers.