@Ryan W, try this instead - you need to look at all possible sequential value sets so a recusive function seems applicable. This could be done as a different named second function (first part of if) called by lengthOfLIS (else part of if):
function [nums] = lengthOfLIS(array,varargin)
if nargin-1 % this is a recursive call so look at all values greater than the last
nums = 0;
for i = find(array>varargin{1})
nums = max(nums,1+lengthOfLIS(array(i+1:end),array(i)));
end
else % this is the first call so look at all initial candidates
nums = 1;
for i = find(array(1:end-1)<array(2:end))
nums = max(nums,1+lengthOfLIS(array(i+1:end),array(i)));
end
end
end
