A325769 Number of integer partitions of n whose distinct consecutive subsequences have different sums.

1, 1, 2, 3, 4, 6, 7, 11, 12, 17, 19, 29, 28, 41, 42, 62, 61, 88, 87, 123, 121, 168, 164, 234, 225, 306, 306, 411, 401, 527, 533, 700, 689, 894, 885, 1163, 1150, 1452, 1469, 1866, 1835, 2333, 2346, 2913, 2913, 3638, 3619, 4511, 4537, 5497, 5576, 6859, 6827, 8263

Offset: 0

Author

Gus Wiseman, May 21 2019

Keywords

• nonn

Comments

For example (3,3,1,1) is counted under a(8) because it has distinct consecutive subsequences (), (1), (1,1), (3), (3,1), (3,1,1), (3,3), (3,3,1), (3,3,1,1), all of which have different sums.

The Heinz numbers of these partitions are given by A325778.

Examples

			The a(1) = 1 through a(8) = 12 partitions:
  (1)  (2)   (3)    (4)     (5)      (6)       (7)        (8)
       (11)  (21)   (22)    (32)     (33)      (43)       (44)
             (111)  (31)    (41)     (42)      (52)       (53)
                    (1111)  (221)    (51)      (61)       (62)
                            (311)    (222)     (322)      (71)
                            (11111)  (411)     (331)      (332)
                                     (111111)  (421)      (521)
                                               (511)      (611)
                                               (2221)     (2222)
                                               (4111)     (3311)
                                               (1111111)  (5111)
                                                          (11111111)
		

Links

• Fausto A. C. Cariboni, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A000041, A002033, A143823, A169942, A325676, A325677, A325683, A325768, A325770, A325778.

Programs

Mathematica

Table[Length[Select[IntegerPartitions[n],UnsameQ@@Total/@Union[ReplaceList[#,{_,s__,_}:>{s}]]&]],{n,0,30}]

Extensions

a(41)-a(53) from Fausto A. C. Cariboni, Feb 24 2021