// output of ./demo/comb/partition-s-desc-demo.cc:
// Description:
//% S-partitions: integer partitions into parts 2^n-1.
//% Representation as weakly descending list of parts.
//% Cf. OEIS sequence A000929.

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