For two non-negative integers $$a$$ and $$b$$ , the equation $${ 3\cdot 2 }^{ a }+1={ b }^{ 2 }$$ has solutions $$({ a }_{ 1 },{ b }_{ 1 }),({ a }_{ 2 },{ b }_{ 2 }),...,({ a }_{ n },{ b }_{ n })$$.
Find $${ a }_{ 1 }{ +b }_{ 1 }+{ a }_{ 2 }+{ b }_{ 2 }+...+{ a }_{ n }+{ b }_{ n }$$?