A Generalization of Very Odd Sequences
Keywords:
very odd sequence, Pelikan’s conjecture
Abstract
Let N be the set of positive integers and n∈N. Let a=(a0,a1,…,an−1) be a sequence of length n, with ai∈{0,1}. For 0≤k≤n−1, let Ak(a)=∑0≤i≤j≤n−1j−i=kaiaj. The sequence a is called a very odd sequence if Ak(a) is odd for all 0≤k≤n−1. In this paper, we study a generalization of very odd sequences and give a characterisation of these sequences.