A367904 - OEIS

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.

1, 2, 6, 38, 666, 32282, 3965886, 1165884638, 792920124786, 1220537093266802, 4187268805038970806, 31649452354183112810198, 522319168680465054600480906, 18683388426164284818805590810122, 1439689660962836496648920949576152046, 237746858936806624825195458794266076911118

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OFFSET

0,2

LINKS

Christian Sievers, Table of n, a(n) for n = 0..77

FORMULA

a(n) = A367902(n) - A367772(n). - Christian Sievers, Jul 26 2024

Binomial transform of A003024. - Christian Sievers, Aug 12 2024

EXAMPLE

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).

The a(0) = 1 through a(2) = 6 set-systems:

{} {} {}

{{1},{2}}

{{1},{1,2}}

{{2},{1,2}}

MATHEMATICA

Table[Length[Select[Subsets[Subsets[Range[n]]], Length[Select[Tuples[#], UnsameQ@@#&]]==1&]], {n, 0, 3}]

CROSSREFS

The maximal case (n subsets) is A003024.

The version for at least one choice is A367902.

The version for no choices is A367903, no singletons A367769, ranks A367907.

These set-systems have ranks A367908, nonzero A367906.

A000372 counts antichains, covering A006126, nonempty A014466.

A003465 counts covering set-systems, unlabeled A055621.

A058891 counts set-systems, unlabeled A000612.

A059201 counts covering T_0 set-systems.

A323818 counts covering connected set-systems, unlabeled A323819.

Cf. A102896, A133686, A283877, A306445, A355741, A367770, A367862, A367869, A367901, A367905.

Sequence in context: A005738 A055704 A005740 * A006536 A057297 A005530

Adjacent sequences: A367901 A367902 A367903 * A367905 A367906 A367907

KEYWORD

nonn

AUTHOR

Gus Wiseman, Dec 08 2023

EXTENSIONS

a(5)-a(8) from Christian Sievers, Jul 26 2024

More terms from Christian Sievers, Aug 12 2024

STATUS

approved