cp's OEIS Frontend

A367904 Number of sets of nonempty subsets of {1..n} with only one possible way to choose a sequence of different vertices of each edge.

%I A367904 #20 Aug 16 2024 08:36:13
%S A367904 1,2,6,38,666,32282,3965886,1165884638,792920124786,1220537093266802,
%T A367904 4187268805038970806,31649452354183112810198,
%U A367904 522319168680465054600480906,18683388426164284818805590810122,1439689660962836496648920949576152046,237746858936806624825195458794266076911118
%N A367904 Number of sets of nonempty subsets of {1..n} with only one possible way to choose a sequence of different vertices of each edge.
%H A367904 Christian Sievers, <a href="/A367904/b367904.txt">Table of n, a(n) for n = 0..77</a>
%F A367904 a(n) = A367902(n) - A367772(n). - _Christian Sievers_, Jul 26 2024
%F A367904 Binomial transform of A003024. - _Christian Sievers_, Aug 12 2024
%e A367904 The set-system Y = {{1},{1,2},{2,3}} has choices (1,1,2), (1,1,3), (1,2,2), (1,2,3), of which only (1,2,3) has all different elements, so Y is counted under a(3).
%e A367904 The a(0) = 1 through a(2) = 6 set-systems:
%e A367904   {}  {}     {}
%e A367904       {{1}}  {{1}}
%e A367904              {{2}}
%e A367904              {{1},{2}}
%e A367904              {{1},{1,2}}
%e A367904              {{2},{1,2}}
%t A367904 Table[Length[Select[Subsets[Subsets[Range[n]]], Length[Select[Tuples[#],UnsameQ@@#&]]==1&]],{n,0,3}]
%Y A367904 The maximal case (n subsets) is A003024.
%Y A367904 The version for at least one choice is A367902.
%Y A367904 The version for no choices is A367903, no singletons A367769, ranks A367907.
%Y A367904 These set-systems have ranks A367908, nonzero A367906.
%Y A367904 A000372 counts antichains, covering A006126, nonempty A014466.
%Y A367904 A003465 counts covering set-systems, unlabeled A055621.
%Y A367904 A058891 counts set-systems, unlabeled A000612.
%Y A367904 A059201 counts covering T_0 set-systems.
%Y A367904 A323818 counts covering connected set-systems, unlabeled A323819.
%Y A367904 Cf. A102896, A133686, A283877, A306445, A355741, A367770, A367862, A367869, A367901, A367905.
%K A367904 nonn
%O A367904 0,2
%A A367904 _Gus Wiseman_, Dec 08 2023
%E A367904 a(5)-a(8) from _Christian Sievers_, Jul 26 2024
%E A367904 More terms from _Christian Sievers_, Aug 12 2024