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 A325325 #19 Feb 27 2021 22:04:28
%S A325325 1,1,2,2,4,5,5,8,11,12,16,22,21,30,34,42,49,64,67,87,95,117,132,160,
%T A325325 169,207,230,274,301,360,395,463,506,602,656,762,834,960,1042,1220,
%U A325325 1311,1505,1643,1859,2000,2341,2491,2827,3083,3464,3747,4302,4561,5154
%N A325325 Number of integer partitions of n with distinct differences between successive parts.
%C A325325 The Heinz numbers of these partitions are given by A325368.
%H A325325 Fausto A. C. Cariboni, <a href="/A325325/b325325.txt">Table of n, a(n) for n = 0..400</a> (terms 0..123 from Alois P. Heinz)
%H A325325 Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts.</a>
%e A325325 The a(0) = 1 through a(9) = 12 partitions:
%e A325325 () (1) (2) (3) (4) (5) (6) (7) (8) (9)
%e A325325 (11) (21) (22) (32) (33) (43) (44) (54)
%e A325325 (31) (41) (42) (52) (53) (63)
%e A325325 (211) (221) (51) (61) (62) (72)
%e A325325 (311) (411) (322) (71) (81)
%e A325325 (331) (332) (441)
%e A325325 (421) (422) (522)
%e A325325 (511) (431) (621)
%e A325325 (521) (711)
%e A325325 (611) (4221)
%e A325325 (4211) (4311)
%e A325325 (5211)
%e A325325 For example, (5,2,1,1) has differences (-3,-1,0), which are distinct, so (5,2,1,1) is counted under a(9).
%t A325325 Table[Length[Select[IntegerPartitions[n],UnsameQ@@Differences[#]&]],{n,0,30}]
%Y A325325 Cf. A007294, A007862, A049988, A098859, A240026, A240027, A320348, A320466, A320470, A325324, A325349, A325352, A325368, A325404, A325468.
%K A325325 nonn
%O A325325 0,3
%A A325325 _Gus Wiseman_, Apr 23 2019