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A018788
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Number of subsets of { 1, ..., n } containing an A.P. of length 3.
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1
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0, 0, 0, 1, 3, 9, 24, 63, 150, 343, 746, 1605, 3391, 7075, 14624, 30076, 61385, 124758, 252618, 510161, 1027632, 2066304, 4148715, 8322113, 16680369, 33413592, 66904484, 133923906, 268009597, 536257466, 1072861536, 2146225299, 4293173040
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OFFSET
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0,5
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LINKS
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Table of n, a(n) for n=0..32.
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FORMULA
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a(n) = 2^n - A051013(n) - David Nacin, Mar 03 2012
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EXAMPLE
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For n=4 the only subsets containing an A.P. of length 3 are {1,2,3},{2,3,4} and {1,2,3,4}. This a(4) = 3. - David Nacin, Mar 03 2012
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PROG
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(Python)
#Prints out all such sets
def containsap3(n):
.ap3list=list()
.for skip in range(1, (n+1)//2):
..for start in range (1, n+1-2*skip):
...ap3list.append(set({start, start+skip, start+2*skip}))
.s=list()
.for i in range(3, n+1):
..for temptuple in comb(range(1, n+1), i):
...tempset=set(temptuple)
...for sub in ap3list:
....if sub <= tempset:
.....s.append(tempset)
.....break
.return s #
#Counts all such sets
def a(n):
.return len(containsap3(n)) # - David Nacin, Mar 03 2012
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CROSSREFS
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Cf. A051013
Sequence in context: A079282 A117585 A006684 * A098690 A090400 A123888
Adjacent sequences: A018785 A018786 A018787 * A018789 A018790 A018791
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KEYWORD
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nonn
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AUTHOR
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David W. Wilson
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STATUS
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approved
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