- #1
ramsey2879
- 841
- 3
define the sequence [tex]P_n[/tex] as follows:
[tex]P_{0} = 1[/tex] ; [tex]P_{1} = a[/tex] and [tex]P_{n} = 6P_{(n-1)}-P_{(n-2)} + 2a^2-8a+4[/tex]
Then each term is a product of two numbers as follows
[tex]P_{n}= {1*1,1*a,a*b,b*c,c*d,d*e,\dots}[/tex]
where
b = 2a-1
c = 4b-a
d = 2c-b
e = 4d-c
f = 2e-d
...
...
Has anyone come across this before
[tex]P_{0} = 1[/tex] ; [tex]P_{1} = a[/tex] and [tex]P_{n} = 6P_{(n-1)}-P_{(n-2)} + 2a^2-8a+4[/tex]
Then each term is a product of two numbers as follows
[tex]P_{n}= {1*1,1*a,a*b,b*c,c*d,d*e,\dots}[/tex]
where
b = 2a-1
c = 4b-a
d = 2c-b
e = 4d-c
f = 2e-d
...
...
Has anyone come across this before