Odd and even sums of generalized Fibonacci numbers by matrix methods
For integers A and B, and positive integers n, we define two generalized Fibonacci
sequence {gn} and {hn}, respectively, by the recurrence relations g n+ 1= Ag n+ gn− 1 and h
n+ 1= hn+ Bh n− 1 where g 0= h 0= 0, g 1= h 1= 1. Using a matrix approach, we obtained the
odd sum and even sum of the two sequences for all values of A and B.
sequence {gn} and {hn}, respectively, by the recurrence relations g n+ 1= Ag n+ gn− 1 and h
n+ 1= hn+ Bh n− 1 where g 0= h 0= 0, g 1= h 1= 1. Using a matrix approach, we obtained the
odd sum and even sum of the two sequences for all values of A and B.