/*

  Number of moves for a leap frog puzzle.

  See leap_frog_puzzle.pi

  For N = 1..15 (go2/0) this program gives these counts (lengths):
    counts=[3,8,15,24,35,48,63,80,99,120,143,168,195,224,255]

  It's http://oeis.org/A005563
  """
  A005563   n*(n+2) (or, (n+1)^2-1)
  ....
  
  This is also the number of moves that it takes n frogs to swap places with n 
  toads on a strip of 2n+1 squares (or positions, or lilypads) where a move is 
  a single slide or jump,
  """

  * Point sequence
    maxCount = 3
    code = (A * (A + 2)) = [[[1],3],[[2],8],[[3],15],[[4],24],[[5],35],[[6],48],[[7],63],[[8],80],[[9],99]] = [[10] = 120]


  * Recursive sequence:

    Order 2:

    data = [[[3,8],15],[[8,15],24],[[15,24],35],[[24,35],48],[[35,48],63],[[48,63],80],[[63,80],99]]
    unknown = [80,99]
    ops = (map)[user = [pow],infix = [+,-,*]]
    constants = [1,2]

    maxCount = 5
    code = ((B + (B + 2)) - A) = [[[3,8],15],[[8,15],24],[[15,24],35],[[24,35],48],[[35,48],63],[[48,63],80],[[63,80],99]] = [[80,99] = 120]
    code = ((2 * (B + 1)) - A) = [[[3,8],15],[[8,15],24],[[15,24],35],[[24,35],48],[[35,48],63],[[48,63],80],[[63,80],99]] = [[80,99] = 120]

*/

data(dots_and_boxes,Data,Vars,Unknown,Ops,Constants,MaxC) :-
  Seq = [3,8,15,24,35,48,63,80,99], % ,120,143,168,195,224,255],
  Ops = new_map([infix=["+","-","*"]
                % , user=["pow"]
                ]), 
  Constants = 1..2,
  MaxC = 5,
  (
    println("point_seq:"),
    make_point_seq(Seq,Data,Unknown,Vars)
   ;
    println("seq:"),
    member(N,1..2),
    println(n=N),
    make_seq(Seq,N,Data,Unknown,Vars)
  ).