漸化式 \(a_{n+2}-qa_{n+1}=p(a_{n+1}-qa_n)\)
逐次的(successive)計算
\(a_{3}-qa_{2}=p(a_{2}-qa_{1})\)
\(a_{4}-qa_{3}=p(a_{3}-qa_{2})=p^2(a_{2}-qa_{1})\)
\(a_{5}-qa_{4}=p(a_{4}-qa_{3})=p^3(a_{2}-qa_{1})\)
\(a_{6}-qa_{5}=p(a_{5}-qa_{4})=p^4(a_{2}-qa_{1})\)
…
\(a_{n+1}-qa_{n}=p(a_{n}-qa_{n-1})=p^{n-1}(a_{2}-qa_{1})\)
\(a_{n+1}-qa_{n}=p(a_{n}-qa_{n-1})\)
\(a_{n}-qa_{n-1}=p(a_{n-1}-qa_{n-2})\), \(a_{n+1}-qa_{n}=p^2(a_{n-1}-qa_{n-2})\)
\(a_{n-1}-qa_{n-2}=p(a_{n-2}-qa_{n-3})\), \(a_{n+1}-qa_{n}=p^3(a_{n-2}-qa_{n-3})\)
…
\(a_{4}-qa_{3}=p(a_{3}-qa_{2})\), \(a_{n+1}-qa_{n}=p^{n-2}(a_{3}-qa_{2})\)
\(a_{3}-qa_{2}=p(a_{2}-qa_{1})\), \(a_{n+1}-qa_{n}=p^{n-1}(a_{2}-qa_{1})\)
逐次的な計算は，項を次々と生成して(generate)いく感覚である。
帰納的な計算は，項の生成されていく過程を辿る感覚である。