/*
  Pochhammer

  From Maple:

 > convert(pochhammer(n,2),factorial);
                                                  (n + 1)!
                                                  --------
                                                  (n - 1)!
 > [seq(%,n=1..10)];
                                  [2, 6, 12, 20, 30, 42, 56, 72, 90, 110]
 > IdentifySequence(%,x);
                                                 (x + 1) x



  Using make_point_seq, data is:
  [[[1],2],[[2],6],[[3],12],[[4],20],[[5],30],[[6],42],[[7],56],[[8],72],[[9],90],[[10],110]] 


  [program = (A + 1) * A,res = 132,count = 99]
  [program = A * A + A,res = 132,count = 97]
  [program = A + A * A,res = 132,count = 96]
  [program = A * (1 + A),res = 132,count = 70]
  [program = A * (A + 1),res = 132,count = 59]
  [program = (1 + A) * A,res = 132,count = 57]
  

  Trying make_seq, i.e. as a recursion
  [[[2],6],[[6],12],[[12],20],[[20],30],[[30],42],[[42],56],[[56],72],[[72],90],[[90],110]]

  make_seq(Seq,1,Data,Unknown,Vars) does not give any solution.

  But with two variables it works:
  data:
  [[[2,6],12],[[6,12],20],[[12,20],30],[[20,30],42],[[30,42],56],[[42,56],72],[[56,72],90],[[72,90],110]]

  make_seq(Seq,2,Data,Unknown,Vars)   
  gives
  [program = 2 - A + (B + B),res = 132,count = 54]
  [program = B + B - (A - 2),res = 132,count = 35]

  [program = 2 + B + (B - A),res = 132,count = 53]
  [program = B - A + (2 + B),res = 132,count = 45]


  And with 3 variables:
  make_seq(Seq,3,Data,Unknown,Vars)   
  [[[2,6,12],20],[[6,12,20],30],[[12,20,30],42],[[20,30,42],56],[[30,42,56],72],[[42,56,72],90],[[56,72,90],110]]

  [program = C - A + (B + 4),res = 132,count = 76]
  [program = C + B - A + 4,res = 132,count = 60]
  [program = 2 * (C + 1) - B,res = 132,count = 51]
  [program = 4 + (C + B - A),res = 132,count = 47]
  [program = C + C - (B - 2),res = 132,count = 36]
  [program = C - (B - (A / A - (4 - 5 - C))) * 1,res = 132.0,count = 7]


*/
data(pochhammer,Data,Vars,Unknown,Ops,Constants,MaxSize,Params) :-
  Seq = [2, 6, 12, 20, 30, 42, 56, 72, 90, 110],
  Ops = [+,-,*,/],
  % make_point_seq(Seq,Data,Unknown,Vars), 
  make_seq(Seq,3,Data,Unknown,Vars), % recursion
  Constants = 1..10, %  ++ [random(-10,10) : _ in 1..10],
  MaxSize = 51,
  Params = new_map([init_size=1000, num_gens=100]).