// output of ./demo/comb/partition-binary-asc-demo.cc:
// Description:
//% Binary partitions as weakly ascending list of parts.
//% Lexicographic order.
//% Cf. OEIS sequences A018819 and A000123.

arg 1: 20 == n  [binary integer partitions of n]  default=20
  1:  [20]   [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ]
  2:  [19]   [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 ]
  3:  [18]   [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 ]
  4:  [17]   [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 ]
  5:  [17]   [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 ]
  6:  [16]   [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 4 ]
  7:  [16]   [ 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 ]
  8:  [15]   [ 1 1 1 1 1 1 1 1 1 1 1 1 2 2 4 ]
  9:  [14]   [ 1 1 1 1 1 1 1 1 1 1 1 1 4 4 ]
 10:  [13]   [ 1 1 1 1 1 1 1 1 1 1 1 1 8 ]
 11:  [15]   [ 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 ]
 12:  [14]   [ 1 1 1 1 1 1 1 1 1 1 2 2 2 4 ]
 13:  [13]   [ 1 1 1 1 1 1 1 1 1 1 2 4 4 ]
 14:  [12]   [ 1 1 1 1 1 1 1 1 1 1 2 8 ]
 15:  [14]   [ 1 1 1 1 1 1 1 1 2 2 2 2 2 2 ]
 16:  [13]   [ 1 1 1 1 1 1 1 1 2 2 2 2 4 ]
 17:  [12]   [ 1 1 1 1 1 1 1 1 2 2 4 4 ]
 18:  [11]   [ 1 1 1 1 1 1 1 1 2 2 8 ]
 19:  [11]   [ 1 1 1 1 1 1 1 1 4 4 4 ]
 20:  [10]   [ 1 1 1 1 1 1 1 1 4 8 ]
 21:  [13]   [ 1 1 1 1 1 1 2 2 2 2 2 2 2 ]
 22:  [12]   [ 1 1 1 1 1 1 2 2 2 2 2 4 ]
 23:  [11]   [ 1 1 1 1 1 1 2 2 2 4 4 ]
 24:  [10]   [ 1 1 1 1 1 1 2 2 2 8 ]
 25:  [10]   [ 1 1 1 1 1 1 2 4 4 4 ]
 26:  [ 9]   [ 1 1 1 1 1 1 2 4 8 ]
 27:  [12]   [ 1 1 1 1 2 2 2 2 2 2 2 2 ]
 28:  [11]   [ 1 1 1 1 2 2 2 2 2 2 4 ]
 29:  [10]   [ 1 1 1 1 2 2 2 2 4 4 ]
 30:  [ 9]   [ 1 1 1 1 2 2 2 2 8 ]
 31:  [ 9]   [ 1 1 1 1 2 2 4 4 4 ]
 32:  [ 8]   [ 1 1 1 1 2 2 4 8 ]
 33:  [ 8]   [ 1 1 1 1 4 4 4 4 ]
 34:  [ 7]   [ 1 1 1 1 4 4 8 ]
 35:  [ 6]   [ 1 1 1 1 8 8 ]
 36:  [ 5]   [ 1 1 1 1 16 ]
 37:  [11]   [ 1 1 2 2 2 2 2 2 2 2 2 ]
 38:  [10]   [ 1 1 2 2 2 2 2 2 2 4 ]
 39:  [ 9]   [ 1 1 2 2 2 2 2 4 4 ]
 40:  [ 8]   [ 1 1 2 2 2 2 2 8 ]
 41:  [ 8]   [ 1 1 2 2 2 4 4 4 ]
 42:  [ 7]   [ 1 1 2 2 2 4 8 ]
 43:  [ 7]   [ 1 1 2 4 4 4 4 ]
 44:  [ 6]   [ 1 1 2 4 4 8 ]
 45:  [ 5]   [ 1 1 2 8 8 ]
 46:  [ 4]   [ 1 1 2 16 ]
 47:  [10]   [ 2 2 2 2 2 2 2 2 2 2 ]
 48:  [ 9]   [ 2 2 2 2 2 2 2 2 4 ]
 49:  [ 8]   [ 2 2 2 2 2 2 4 4 ]
 50:  [ 7]   [ 2 2 2 2 2 2 8 ]
 51:  [ 7]   [ 2 2 2 2 4 4 4 ]
 52:  [ 6]   [ 2 2 2 2 4 8 ]
 53:  [ 6]   [ 2 2 4 4 4 4 ]
 54:  [ 5]   [ 2 2 4 4 8 ]
 55:  [ 4]   [ 2 2 8 8 ]
 56:  [ 3]   [ 2 2 16 ]
 57:  [ 5]   [ 4 4 4 4 4 ]
 58:  [ 4]   [ 4 4 4 8 ]
 59:  [ 3]   [ 4 8 8 ]
 60:  [ 2]   [ 4 16 ]
 ct=60
