m-LUCAS NUMBERS AND m-(MY12)~p NUMBERS

摘要

In this paper m-Lucas sequence is defined, which is the generalization of 2-Lucas sequence. In 2-Lucas sequence every term from third term, is a sum of previous two terms given the first number as 1 and the second number as 3. Further a new and special kind of sequence, which is the extension of m-Fibonacci and m-Lucas sequence is introduced and this is denoted by m- (MY12)~P sequence, where MY12 denotes Mathematics Year 2012. when p = 1, m-(MY12)~1 is a m-bonacci sequence and when p = 3, m-(MY12)~3 is a m-Lucas sequence. The formulae for the sum of n-terms of m-Lucas sequence and m-(MY12)~P sequence, where p ∈ N, p ≠ 1, 2 are found out, similar to m-Bonacci sequence [1].