The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A178173 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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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.
(history; published version)

#18 by Susanna Cuyler at Thu May 20 08:19:49 EDT 2021

STATUS

proposed

approved

#17 by F. Chapoton at Thu May 20 07:06:30 EDT 2021

STATUS

editing

proposed

#16 by F. Chapoton at Thu May 20 07:06:23 EDT 2021

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)

.

from sets import Set

from numpy import array

def toBinary(n, k):

ans=[]

for i in range(k):

ans.insert(0, n%2)

n=n>>1

return array(ans)

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

.... print (i, courcelle(array([4]*i), powerSet(i), exact=False))

STATUS

approved

editing

Discussion

Thu May 20

07:06

F. Chapoton: trying to clean py code

#15 by Susanna Cuyler at Sat Jan 04 14:46:30 EST 2020

STATUS

proposed

approved

#14 by Andrew Howroyd at Sat Jan 04 14:29:09 EST 2020

STATUS

editing

proposed

#13 by Andrew Howroyd at Sat Jan 04 14:11:08 EST 2020

DATA

1, 2, 8, 128, 11087, 2232875, 775098224, 428188962261, 355916994389700, 425272149099677521, 703909738878615927739, 1565842283246869237505246, 4565002967677134523844716754, 17076464900445281560851997140670, 80494979734877344662882495100752511

LINKS

Andrew Howroyd, <a href="/A178173/b178173.txt">Table of n, a(n) for n = 0..50</a>

PROG

(PARI) \\ See A330964 for efficient code to compute this sequence. - Andrew Howroyd, Jan 04 2020

CROSSREFS

Row n=4 of A330964.

KEYWORD

nonn,hard,more

nonn

EXTENSIONS

Terms a(9) and beyond from Andrew Howroyd, Jan 04 2020

STATUS

approved

editing

#12 by N. J. A. Sloane at Sat Dec 07 12:18:26 EST 2019

PROG

....for i in xrangerange(0, k).:

def powerSet(k): return [toBinary(n, k) for n in xrangerange(1, 2**k)]

for i in xrangerange(10):

Discussion

Sat Dec 07

12:18

OEIS Server: https://oeis.org/edit/global/2837

#11 by Alois P. Heinz at Tue Sep 10 17:54:47 EDT 2019

STATUS

proposed

approved

#10 by Bert Dobbelaere at Tue Sep 10 17:34:34 EDT 2019

STATUS

editing

proposed

#9 by Bert Dobbelaere at Tue Sep 10 17:27:52 EDT 2019

CROSSREFS

Replacing limit of 2 with a limit of 1 gives the Bell numbers A000110, limit of 2 gives A178165, limit of 3 gives A178171.

KEYWORD

nonn,hard,changedmore