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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. 3
 1, 2, 8, 128, 11087, 2232875, 775098224, 428188962261, 355916994389700, 425272149099677521, 703909738878615927739, 1565842283246869237505246, 4565002967677134523844716754, 17076464900445281560851997140670, 80494979734877344662882495100752511 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Andrew Howroyd, Table of n, a(n) for n = 0..50 PROG (Python) from sets  import Set from numpy.import.array def.toBinary(n, k): ....ans=[] ....for i in range(0, k).: ........ans.insert(0, n%2) ........n=n>>1 ....return array(ans) . (Python) def powerSet(k): return [toBinary(n, k) for n in range(1, 2**k)] def.courcelle(.maxUses, .remainingSets, .exact=False.).: ....if exact and not all(maxUses<=sum(remainingSets)): ans=0 ....elif len(remainingSets)==0: ans=1 ....else: ........set0=remainingSets[0] ........if all(set0<=maxUses): ans=courcelle(maxUses-set0, remainingSets[1:], exact=exact) ........else: ans=0 ........ans+=courcelle(maxUses, remainingSets[1:], exact=exact) ....return ans for i in range(10): ....print i, courcelle(array([4]*i), powerSet(i), exact=False) (PARI) \\ See A330964 for efficient code to compute this sequence. - Andrew Howroyd, Jan 04 2020 CROSSREFS Row n=4 of A330964. Replacing limit of 2 with a limit of 1 gives the Bell numbers A000110, limit of 2 gives A178165, limit of 3 gives A178171. Sequence in context: A011822 A307124 A111179 * A058891 A274171 A184945 Adjacent sequences:  A178170 A178171 A178172 * A178174 A178175 A178176 KEYWORD nonn AUTHOR Daniel E. Loeb, Dec 17 2010 EXTENSIONS a(6)-a(8) from Bert Dobbelaere, Sep 10 2019 Terms a(9) and beyond from Andrew Howroyd, Jan 04 2020 STATUS approved

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Last modified January 19 21:47 EST 2020. Contains 331066 sequences. (Running on oeis4.)