// 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