A NOTE ON DIFFERENCE SEQUENCES
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초록
It is well known that for a sequence a = (a₀, a₁,...) the general term of the dual sequence of a is [수식], where c = (c₀,...,cn is the dual sequence of a. In this paper, we find the general term of the sequence (c₀, c₁,...) and give another method for finding the inverse matrix of the Pascal matrix. And we find a simple proof of the fact that if the general term of a sequence a = (a₀, a₁,...) is a polynomial of degree p in n, then △p+1a = 0.
Abstract
It is well known that for a sequence a = (a₀, a₁,...) the general term of the dual sequence of a is [수식], where c = (c₀,...,cn is the dual sequence of a. In this paper, we find the general term of the sequence (c₀, c₁,...) and give another method for finding the inverse matrix of the Pascal matrix. And we find a simple proof of the fact that if the general term of a sequence a = (a₀, a₁,...) is a polynomial of degree p in n, then △p+1a = 0.
참고문헌 (2)
- R. A. Brualdi, "A Introductory Combinatorics" (1997), North-Holland
- G. S. Call, "Pascal's matrices", Amer. Math. Monthly, 200, pp.372~376 (1993)