This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A325769 #14 Feb 25 2021 02:27:04
%S A325769 1,1,2,3,4,6,7,11,12,17,19,29,28,41,42,62,61,88,87,123,121,168,164,
%T A325769 234,225,306,306,411,401,527,533,700,689,894,885,1163,1150,1452,1469,
%U A325769 1866,1835,2333,2346,2913,2913,3638,3619,4511,4537,5497,5576,6859,6827,8263
%N A325769 Number of integer partitions of n whose distinct consecutive subsequences have different sums.
%C A325769 For example (3,3,1,1) is counted under a(8) because it has distinct consecutive subsequences (), (1), (1,1), (3), (3,1), (3,1,1), (3,3), (3,3,1), (3,3,1,1), all of which have different sums.
%C A325769 The Heinz numbers of these partitions are given by A325778.
%H A325769 Fausto A. C. Cariboni, <a href="/A325769/b325769.txt">Table of n, a(n) for n = 0..300</a>
%e A325769 The a(1) = 1 through a(8) = 12 partitions:
%e A325769 (1) (2) (3) (4) (5) (6) (7) (8)
%e A325769 (11) (21) (22) (32) (33) (43) (44)
%e A325769 (111) (31) (41) (42) (52) (53)
%e A325769 (1111) (221) (51) (61) (62)
%e A325769 (311) (222) (322) (71)
%e A325769 (11111) (411) (331) (332)
%e A325769 (111111) (421) (521)
%e A325769 (511) (611)
%e A325769 (2221) (2222)
%e A325769 (4111) (3311)
%e A325769 (1111111) (5111)
%e A325769 (11111111)
%t A325769 Table[Length[Select[IntegerPartitions[n],UnsameQ@@Total/@Union[ReplaceList[#,{___,s__,___}:>{s}]]&]],{n,0,30}]
%Y A325769 Cf. A000041, A002033, A143823, A169942, A325676, A325677, A325683, A325768, A325770, A325778.
%K A325769 nonn
%O A325769 0,3
%A A325769 _Gus Wiseman_, May 21 2019
%E A325769 a(41)-a(53) from _Fausto A. C. Cariboni_, Feb 24 2021