// output of ./demo/seq/A003043-demo.cc:
// Description:
//% OEIS sequence A003043:
//% Number of Hamiltonian paths (or Gray codes) on n-cube with a marked starting node.
//% Computation as Permutations with restricted prefixes.
//% Also A059783: paths from vec(0) to vec(1).

arg 1: 8 == n  [Permutations of {1, 2, ..., n}]  default=8
arg 2: 0 == c  [Condition function: 
      (0: A003043, Hamiltonian paths),
      (1: A059783, paths from vec(0) to vec(1))]  default=0
A003043, Hamiltonian paths:
   1:  [ 0 1 3 2 6 4 5 7 ]
   2:  [ 0 1 3 2 6 7 5 4 ]
   3:  [ 0 1 3 7 5 4 6 2 ]
   4:  [ 0 1 5 4 6 2 3 7 ]
   5:  [ 0 1 5 4 6 7 3 2 ]
   6:  [ 0 1 5 7 3 2 6 4 ]
   7:  [ 0 2 3 1 5 4 6 7 ]
   8:  [ 0 2 3 1 5 7 6 4 ]
   9:  [ 0 2 3 7 6 4 5 1 ]
  10:  [ 0 2 6 4 5 1 3 7 ]
  11:  [ 0 2 6 4 5 7 3 1 ]
  12:  [ 0 2 6 7 3 1 5 4 ]
  13:  [ 0 4 5 1 3 2 6 7 ]
  14:  [ 0 4 5 1 3 7 6 2 ]
  15:  [ 0 4 5 7 6 2 3 1 ]
  16:  [ 0 4 6 2 3 1 5 7 ]
  17:  [ 0 4 6 2 3 7 5 1 ]
  18:  [ 0 4 6 7 5 1 3 2 ]
 ct=18