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A178173 Number of collections of nonempty subsets of an n-element set where each element appears in at most 4 subsets.

%I A178173 #23 Jul 21 2025 00:24:12
%S A178173 1,2,8,128,11087,2232875,775098224,428188962261,355916994389700,
%T A178173 425272149099677521,703909738878615927739,1565842283246869237505246,
%U A178173 4565002967677134523844716754,17076464900445281560851997140670,80494979734877344662882495100752511
%N A178173 Number of collections of nonempty subsets of an n-element set where each element appears in at most 4 subsets.
%H A178173 Andrew Howroyd, <a href="/A178173/b178173.txt">Table of n, a(n) for n = 0..50</a>
%o A178173 (Python)
%o A178173 from numpy import array
%o A178173 def toBinary(n,k):
%o A178173     ans=[]
%o A178173     for i in range(k):
%o A178173         ans.insert(0,n%2)
%o A178173         n=n>>1
%o A178173     return array(ans)
%o A178173 def powerSet(k): return [toBinary(n,k) for n in range(1,2**k)]
%o A178173 def courcelle(maxUses,remainingSets,exact=False):
%o A178173     if exact and not all(maxUses<=sum(remainingSets)): ans=0
%o A178173     elif len(remainingSets)==0: ans=1
%o A178173     else:
%o A178173         set0=remainingSets[0]
%o A178173         if all(set0<=maxUses): ans=courcelle(maxUses-set0,remainingSets[1:],exact=exact)
%o A178173         else: ans=0
%o A178173         ans+=courcelle(maxUses,remainingSets[1:],exact=exact)
%o A178173     return ans
%o A178173 for i in range(10):
%o A178173     print(i, courcelle(array([4]*i),powerSet(i),exact=False))
%o A178173 (PARI) \\ See A330964 for efficient code to compute this sequence. - _Andrew Howroyd_, Jan 04 2020
%Y A178173 Row n=4 of A330964.
%Y A178173 Replacing limit of 2 with a limit of 1 gives the Bell numbers A000110, limit of 2 gives A178165, limit of 3 gives A178171.
%K A178173 nonn
%O A178173 0,2
%A A178173 _Daniel E. Loeb_, Dec 17 2010
%E A178173 a(6)-a(8) from _Bert Dobbelaere_, Sep 10 2019
%E A178173 Terms a(9) and beyond from _Andrew Howroyd_, Jan 04 2020