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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 A349077 A188978 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 February 28 16:19 EST 2024. Contains 370400 sequences. (Running on oeis4.)