Korean J. Math.  Vol 27, No 3 (2019)  pp.723-734
DOI: https://doi.org/10.11568/kjm.2019.27.3.723

Diagonal sums in negative trinomial table

Eunmi Choi, Yuna Oh


We study the negative trinomial table $T'$ of $(x^2+x+1)^{-n}$  and its $t/u$-slope diagonals for any $t,u > 0$.  We investigate recurrence formula of the $t/u$-slope diagonal sums of $T'$  and find interrelationships with $t/u$-slope diagonal sums of the trinomial table $T$.


trinomial table, tribonacci sequence, diagonal sum

Subject classification

05A10, 11R11


Full Text:



E. Choi, Diagonal sums of negative pascal table, JP Journal of Algebra, Number Theory and Applications 39 (2017), 457–477. (Google Scholar)

V. E. Hoggatt and M. Bicknell, Diagonal sums of the trinomial triangle, Fibo. Quart. 12 (1974), 47–50. (Google Scholar)

K. Kuhapatanakul and L. Sukruan, The generalized tribonacci numbers with negative subscripts, Integers 14 (2014), A32. (Google Scholar)

K. Kuhapatanakul and L. Sukruan, n-tribonacci triangles and applications, Int. J. Math. Edu. in Science and Technology, 45 (7) (2014), 1068–1113. (Google Scholar)

E. Kilic, Tribonacci sequences with certain indices and their sums, Ars. Comb. 86 (2008), 13–22. (Google Scholar)

J. Lee, A note on the negative Pascal triangle, Fibo. Quart. 32 (1994), 269–270. (Google Scholar)

C.W. Puritz, Extending Pascal’s triangle upwards, Math. Gaz. 65 (431) (1981), 42–22. (Google Scholar)


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