% Generalizes notes12.L33.pl for instance size

myappend([], Ys, Ys).
myappend([X|Xs], Ys, [X|Zs]) :- myappend(Xs, Ys, Zs).

mysublist(Xs, Ys) :- myappend(As, XsBs, Ys), myappend(Xs, Bs, XsBs).

list_of_n(0,[]) :- !.
list_of_n(1,[_]) :- !.
list_of_n(N,[_|X]) :- N1 is N-1, list_of_n(N1,X), !.

sublist_for_n(N,Res) :- list_of_n(N,First), list_of_n(N,Second),
  myappend([N],First,Nfirst), myappend([N],Second,Nsecond),
  myappend(Nfirst,Nsecond,Nthird), myappend(Nthird,[N],Res).

mysublistgen(0,Ls) :- sublist_for_n(0,Sub), mysublist(Sub,Ls), !. %0s are included
mysublistgen(N,Ls) :- sublist_for_n(N,Sub), mysublist(Sub,Ls), N1 is N-1,
                      mysublistgen(N1,Ls).

% N+1 is the number of triples since 0,0,0 is included
sol(N,Ls) :-
  I is 3*(N+1), list_of_n(I,Ls), % 0s are included
  mysublistgen(N,Ls).