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A113896 Number of maximal (and largest) superset towers with n base elements. 0
1, 4, 864, 2579890176 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

On 3 elements ABC, some tower (Halmos, "Naive Set Theory" among many) that begins with the empty set can be written without loss of generality as {0, A, AB, ABC}. But we need to have sets B, C, BC, AC included somewhere too so that the thing is "largest", i.e., includes every subset of {A,B,C}. For ABCD, there are 3^3 ways to include B,C,D into AB,AC,AD,BC,BD,CD and 2^5 ways to include AC,AD,BC,BD,CD into ABC,ABD,ACD,BCD. So a(4) = 3^3*2^5.

LINKS

Table of n, a(n) for n=0..3.

FORMULA

(n-1)^(n-1) * (n-2)^(nC2 - 1) * (n-3)^(nC3 - 1) *...* 2^(nC(n-2) - 1) * 1^(n-1)

EXAMPLE

a(2) = 4 because:

(1) 0->A A->AB B->AB C->AB AB->ABC AC->ABC BC->ABC ABC->ABC maximal

(2) 0->A A->AB B->AB C->AC AB->ABC AC->ABC BC->ABC ABC->ABC maximal

(3) 0->A A->AB B->AC C->AB AB->ABC AC->ABC BC->ABC ABC->ABC maximal

(4) 0->A A->AB B->AC C->AC AB->ABC AC->ABC BC->ABC ABC->ABC maximal

CROSSREFS

Sequence in context: A221232 A272167 A255269 * A159706 A188978 A333502

Adjacent sequences:  A113893 A113894 A113895 * A113897 A113898 A113899

KEYWORD

nonn

AUTHOR

Lee Corbin (lcorbin(AT)tsoft.com), Jan 28 2006

STATUS

approved

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Last modified May 25 19:30 EDT 2020. Contains 334595 sequences. (Running on oeis4.)