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

0,4

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.

Links

Table of n, a(n) for n=0..55.

Example

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)

Mathematica

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

Crossrefs

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

Sequence in context: A364349 A364533 A090492 * A371736 A371794 A239949

Adjacent sequences: A325765 A325766 A325767 * A325769 A325770 A325771

Keyword

nonn

Author

Gus Wiseman, May 21 2019

Status

approved