( 1 , k ) - Compositions
نویسندگان
چکیده
A (1, k)-composition of a positive integer n consists of an ordered sequence of the integers 1 and k whose sum is n. A palindromic (1, k)-composition is one for which the sequence is the same from left to right as from right to left. We give recursive equations and generating functions for the total number of such compositions and palindromes, and for the number of 1’s, k’s, “+”signs and summands in all (1, k)-compositions and (1, k)-palindromes. We look at patterns in the values for the total number of (1, k)-compositions and (1, k)-palindromes and derive recusive relations and generating functions for the number of levels, rises and drops in all (1, k)-compositions and (1, k)-palindromes.
منابع مشابه
Compositions of N with No Occurrence of K
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