A325768 - OEIS

%I #5 May 22 2019 21:00:51

%S 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,

%T 100,124,128,152,167,198,212,255,269,315,343,392,428,501,529,615,665,

%U 757,812,937,1002,1142,1238,1385,1490,1701,1808,2038,2200,2476

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

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

%C The Heinz numbers of these partitions are given by A325779.

%e The a(1) = 1 through a(9) = 8 partitions:

%e   (1)  (2)  (3)   (4)   (5)   (6)   (7)    (8)    (9)

%e             (21)  (31)  (32)  (42)  (43)   (53)   (54)

%e                         (41)  (51)  (52)   (62)   (63)

%e                                     (61)   (71)   (72)

%e                                     (421)  (521)  (81)

%e                                                   (432)

%e                                                   (531)

%e                                                   (621)

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

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

%K nonn

%O 0,4

%A _Gus Wiseman_, May 21 2019