p. 251 - 253 A closed-form expression for second-order recurrences
E. Haji-Esmaili and S. H. Ghaderi Received: June 10, 2010;
Accepted: March 17, 2011
Abstract.
This paper introduces a closed-form expression for the
second-order recurrence relation a = _{n}c_{1}a _{n - 1}
+ c_{2}a _{n - 2},
in which c_{1} and c_{2} are fixed constants and the value of two
arbitrary terms a _{n - p} and a _{n - q}
are known where p and q are positive integers and p > q. This expression is
Keywords:
Second-order recurrence; characteristic polynomial;
closed-form solution.
AMS Subject classification:
Primary: 11B37, 11B39.
PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2011, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |