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%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
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