Explicit Formulae for Some Sums of Trinomial Coefficients

yanapat tongron, Takao Komatsu

Abstract


For , and , explicit formulae for , where the sum is over all non-negative integers  such that , are established by Carlitz [1] via properties of the cube root of unity. In this paper, another method to get these formulae is presented. Almost all  are also expressed in terms of the cube root of unity.

Mathematics Subject Classification: 05A10, 11B65


Keywords


sum, trinomial coefficient, cube root of unity, matrix

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