A325768 Number of integer partitions of n for which every restriction to a subinterval has a different sum.

1, 1, 1, 2, 2, 3, 3, 5, 5, 8, 7, 11, 12, 15, 15, 23, 22, 29, 32, 40, 42, 55, 56, 71, 75, 92, 100, 124, 128, 152, 167, 198, 212, 255, 269, 315, 343, 392, 428, 501, 529, 615, 665, 757, 812, 937, 1002, 1142, 1238, 1385, 1490, 1701, 1808, 2038, 2200, 2476

Offset: 0

Author

Gus Wiseman, May 21 2019

Keywords

• nonn

Comments

Also the number of Golomb rulers of length n whose consecutive marks are separated by weakly decreasing distances.

The Heinz numbers of these partitions are given by A325779.

Examples

			The a(1) = 1 through a(9) = 8 partitions:
  (1)  (2)  (3)   (4)   (5)   (6)   (7)    (8)    (9)
            (21)  (31)  (32)  (42)  (43)   (53)   (54)
                        (41)  (51)  (52)   (62)   (63)
                                    (61)   (71)   (72)
                                    (421)  (521)  (81)
                                                  (432)
                                                  (531)
                                                  (621)
		

Crossrefs

Cf. A000041, A002033, A103300, A143823, A169942, A325676, A325687, A325769, A325779.

Programs

Mathematica

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