I'm want to build a game (with steps) that the solution have a Recurrence relation, i.e. - to solve the game you have to move from point A to point B, from point B to point C...(kind of a maze).
Of course that will be a few ways to each point, and the player should choose the way with the amount of the steps by the Recurrence relation...
What I need?
I need few Recurrence relations (something like 4) that all the first 15 elements (it can be less the 15) are between $3-50$
I try to find few, but there was problems:
$x(n)= 2*x(n-1)$ - if I choose $x(0)>0$ the numbers are getting higher too much fast...
$x(n)=2*x(n-1)-x(n-2)$ - Too much easy to solve (from few examples...).
(I took those examples from a site...)
Can you help me and give me few examples?
Thank you!
This python script tests relations in the form $x_{n+1}=ax_n+bn+c$.
An example:
1 -1 8 3 [3, 9, 14, 18, 21, 23, 24, 24, 23, 21, 18, 14, 9, 3]$x_n=x_{n-1}-n+8,\ x_1=3$ yields the above sequence (in bracets).Or this
1 1 -5 11 [11, 8, 6, 5, 5, 6, 8, 11, 15, 20, 26, 33, 41, 50]