Closed-form solutions of general second order linear recurrences and applications |
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| Institution: | 1. Department of Mathematics, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand;2. Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand |
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| Abstract: | Two closed-form solutions of a general second order linear recurrence with variable coefficients are established. The first form is combinatorial in nature and is derived through the use of a set which counts the number of elements which are two units apart. The second form is closely related to continued fractions and is derived through the use of continued fraction-like relation. Several applications including a number of verifications of conjectures produced from the Ramanujan Machine are worked out, which illustrate its versatility in this respect. |
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| Keywords: | Second order linear recurrence with variable coefficient Continued fraction Ramanujan Machine |
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