ZHAO Yuan-e1, LIU Zhuo2
(1 College of Mathematics and Computer Science, Yan′an University, Yan′an 716000, Shaanxi, China;2 Department of Mathematics, Northwest University,Xi′an 710127, Shaanxi, China)
Abstract:
Smarandache-Pascal inverse-derived sequence is introduced, the properties of the Smarandache-Pascal inverse-derived sequence are studied, some interesting identities are obtained by using the elementary and combinational method, and it is proved that if the base sequence {Tn} is a second-order linear recurrence sequence, then its Smarandache-Pascal inverse-derived subsequence is a second-order linear recurrence sequence.Moreover,if the base sequence {Tdn+1} is a subset of the second-order linear recurrence sequence {Tn}, then its Smarandache-Pascal inverse-derived sequence {bn} has a simple linear recurrence expression.
KeyWords:
Smarandache-Pascal derived sequence; inverse sequence; second-order linear recurrence sequence; combinational method; identity
