login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A066369 Number of subsets of {1, ..., n} with no four terms in arithmetic progression. 1
1, 2, 4, 8, 15, 29, 56, 103, 192, 364, 668, 1222, 2233, 3987, 7138, 12903, 22601, 40200, 71583, 125184, 218693, 386543, 670989, 1164385, 2021678, 3462265, 5930954, 10189081, 17266616, 29654738, 50912618 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..30.

EXAMPLE

a(5) = 29 because there are 32 subsets and three of them contain four terms in arithmetic progression: {1, 2, 3, 4}, {2, 3, 4, 5} and {1, 2, 3, 4, 5}.

PROG

(Python)

def noap4(n):

.avoid=list()

.for skip in range(1, (n+2)//3):

..for start in range (1, n+1-3*skip):

...avoid.append(set({start, start+skip, start+2*skip, start+3*skip}))

.s=list()

.for i in range(4):

..for smallset in comb(range(1, n+1), i):

...s.append(smallset)

.for i in range(4, n+1):

..for temptuple in comb(range(1, n+1), i):

...tempset=set(temptuple)

...status=True

...for avoidset in avoid:

....if avoidset <= tempset:

.....status=False

.....break

...if status:

....s.append(tempset)

.return s

#Counts all such sets

def a(n):

.return len(noap4(n)) #-David Nacin, Mar 05 2012

CROSSREFS

Cf. A051013,A018789

Sequence in context: A208976 A224959 A108564 * A239555 A275544 A000078

Adjacent sequences:  A066366 A066367 A066368 * A066370 A066371 A066372

KEYWORD

nonn

AUTHOR

Jan Kristian Haugland (jankrihau(AT)hotmail.com), Dec 22 2001

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 10 23:13 EST 2016. Contains 279021 sequences.