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A325768 Number of integer partitions of n for which every restriction to a subinterval has a different sum. 17
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 (list; graph; refs; listen; history; text; internal format)
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: A244800 A275972 A090492 * A239949 A103609 A237800

Adjacent sequences:  A325765 A325766 A325767 * A325769 A325770 A325771

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 21 2019

STATUS

approved

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Last modified July 4 16:24 EDT 2020. Contains 335448 sequences. (Running on oeis4.)