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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.)