This work brings representations of palindromic and number patterns in terms of single letter "a". Some examples of prime patterns are also considered. Different classifications of palindromic patterns are considered, such as palindromic decomposition, double symmetric patterns, number patterns decompositions, etc. Number patterns with powers are also studied. Some extensions to Pythagorean triples are also given. Study towards Fibonacci sequence and its extensions are also made. This work is revised and enlarged version of author's previous work done in 2015.