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 A325099 #6 Jul 27 2019 14:57:51
%S A325099 1,1,1,1,2,2,3,1,4,5,8,6,11,11,15,13,18,20,30,29,43,49,68,66,84,94,
%T A325099 125,131,165,184,237,251,291,315,383,408,486,536,663,714,832,912,1104,
%U A325099 1195,1405,1554,1877,2046,2348,2559,2998,3256,3730,4084,4793,5230,5938
%N A325099 Number of binary carry-connected strict integer partitions of n.
%C A325099 A binary carry of two positive integers is an overlap of the positions of 1's in their reversed binary expansion. An integer partition is binary carry-connected if the graph whose vertices are the parts and whose edges are binary carries is connected.
%e A325099 The a(1) = 1 through a(11) = 6 strict partitions (A = 10, B = 11):
%e A325099 (1) (2) (3) (4) (5) (6) (7) (8) (9) (A) (B)
%e A325099 (31) (32) (51) (53) (54) (64) (65)
%e A325099 (321) (62) (63) (73) (74)
%e A325099 (71) (72) (91) (632)
%e A325099 (531) (532) (731)
%e A325099 (541) (5321)
%e A325099 (631)
%e A325099 (721)
%t A325099 binpos[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A325099 csm[s_]:=With[{c=Select[Tuples[Range[Length[s]],2],And[OrderedQ[#],UnsameQ@@#,Length[Intersection@@s[[#]]]>0]&]},If[c=={},s,csm[Sort[Append[Delete[s,List/@c[[1]]],Union@@s[[c[[1]]]]]]]]];
%t A325099 Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&Length[csm[binpos/@#]]<=1&]],{n,0,30}]
%Y A325099 Cf. A050315, A080572, A247935, A267610, A267700.
%Y A325099 Cf. A325095, A325096, A325098, A325104, A325106, A325110, A325119.
%K A325099 nonn
%O A325099 0,5
%A A325099 _Gus Wiseman_, Mar 28 2019