Journal of Integer Sequences, Vol. 21 (2018), Article 18.7.3

The Trinomial Transform Triangle

László Németh
Institute of Mathematics
University of Sopron
Bajcsy Zs. u. 4
Sopron H9400


The trinomial transform of a sequence is a generalization of the well-known binomial transform, replacing binomial coefficients with trinomial coefficients. We examine Pascal-like triangles under the trinomial transform, focusing on ternary linear recurrent sequences. We determine the sums and alternating sums of the elements in columns, and we give some examples of the trinomial transform triangle.

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(Concerned with sequences A000012 A000045 A000073 A000244 A001477 A002378 A003462 A014983 A027907 A033999 A036290 A038608 A082761 A097861 A097893 A097894 A192806.)

Received January 9 2018; revised version received May 7 2018; May 23 2018; July 16 2018. Published in Journal of Integer Sequences, August 23 2018.

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