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Diagonal sums in negative trinomial table
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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 $T$.
Abstract
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 $T$.
참고문헌 (7)
- E. Choi, "Diagonal sums of negative pascal table", JP Journal of Algebra, Number Theory and Applications, 39, pp.457~477 (2017)
- V. E. Hoggatt, "Diagonal sums of the trinomial triangle", Fibo. Quart, 12, pp.47~50 (1974)
- K. Kuhapatanakul, "The generalized tribonacci numbers with negative subscripts", Integers, 14, pp.A32~ (2014)
- K. Kuhapatanakul, "n-tribonacci triangles and applications", Int. J. Math. Edu. in Science and Technology, 45(7), pp.1068~1113 (2014)
- E. Kilic, "Tribonacci sequences with certain indices and their sums", Ars. Comb, 86, pp.13~22 (2008)
- J. Lee, "A note on the negative Pascal triangle", Fibo. Quart, 32, pp.269~270 (1994)
- C. W. Puritz, "Extending Pascal's triangle upwards", Math. Gaz, 65(431), pp.42~22 (1981)
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