Explicit Formulae for Some Sums of Trinomial Coefficients
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Published:
Jun 22, 2020
Keywords:
sum trinomial coefficient cube root of unity matrix
Main Article Content
Abstract
For a,b,c∈{0,1,2},n∈,n≥a+b+c, and n≡a+b+c (mod 3), explicit formulae for
, where the sum is over all non-negative integers i,j,k such that n=i+j+k, 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
Article Details
How to Cite
1.
Tongron Y, Komatsu T. Explicit Formulae for Some Sums of Trinomial Coefficients. Prog Appl Sci Tech. [Internet]. 2020 Jun. 22 [cited 2024 Nov. 15];10(1):161-9. Available from: https://ph02.tci-thaijo.org/index.php/past/article/view/242916
Section
Mathematics and Applied Statistics
References
Carlitz L. Some sums of multinomial coefficients. Fibonacci Quart. 1976. 14 : 427-438.
Fixman U. Sums of multinomial coefficients. Canad. Math. Bull. 1988. 31(2) : 187-189.
Hoggatt V. E., Jr. and Alexanderson G. L. Sums of partition sets in generalized Pascal triangles I. Fibonacci Quart. 1976. 14(2) : 117-125.