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 A018788 Number of subsets of { 1, ..., n } containing an A.P. of length 3. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS FORMULA a(n) = 2^n - A051013(n) - David Nacin, Mar 03 2012 EXAMPLE 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 PROG (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 CROSSREFS Cf. A051013 Sequence in context: A079282 A117585 A006684 * A098690 A090400 A123888 Adjacent sequences:  A018785 A018786 A018787 * A018789 A018790 A018791 KEYWORD nonn AUTHOR STATUS approved

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