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 A356235 #7 Aug 25 2022 08:33:36
%S A356235 0,1,1,1,2,3,5,8,12,16,25,33,45,62,84,109,148,192,251,325,421,536,690,
%T A356235 870,1100,1385,1739,2161,2697,3334,4121,5071,6228,7609,9303,11308,
%U A356235 13732,16629,20101,24206,29140,34957,41882,50060,59745,71124,84598,100365
%N A356235 Number of integer partitions of n with a neighborless singleton.
%C A356235 A part x is neighborless if neither x - 1 nor x + 1 are parts, and a singleton if it appears only once. Examples of partitions with a neighborless singleton are: (3), (3,1), (3,1,1), (3,3,1). Examples of partitions without a neighborless singleton are: (3,3,1,1), (4,3,1,1), (3,2,1), (2,1), (3,3).
%e A356235 The a(1) = 1 through a(8) = 12 partitions:
%e A356235 (1) (2) (3) (4) (5) (6) (7) (8)
%e A356235 (31) (41) (42) (52) (53)
%e A356235 (311) (51) (61) (62)
%e A356235 (411) (331) (71)
%e A356235 (3111) (421) (422)
%e A356235 (511) (431)
%e A356235 (4111) (521)
%e A356235 (31111) (611)
%e A356235 (4211)
%e A356235 (5111)
%e A356235 (41111)
%e A356235 (311111)
%t A356235 Table[Length[Select[IntegerPartitions[n],Min@@Length/@Split[Reverse[#],#1>=#2-1&]==1&]],{n,0,30}]
%Y A356235 The complement is counted by A355393.
%Y A356235 This is the singleton case of A356236, complement A355394.
%Y A356235 These partitions are ranked by A356237.
%Y A356235 The strict case is A356607, complement A356606.
%Y A356235 A000041 counts integer partitions, strict A000009.
%Y A356235 A000837 counts relatively prime partitions, ranked by A289509.
%Y A356235 A007690 counts partitions with no singletons, complement A183558.
%Y A356235 Cf. A066205, A325160, A328171, A328172, A328187, A328221, A356233.
%K A356235 nonn
%O A356235 0,5
%A A356235 _Gus Wiseman_, Aug 23 2022