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 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, 86017601, 145327544, 247555043, 415598432, 698015188 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA a(n) = 2^n - A018789(n). 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: A335473 A224959 A108564 * A239555 A275544 A000078 Adjacent sequences:  A066366 A066367 A066368 * A066370 A066371 A066372 KEYWORD nonn AUTHOR Jan Kristian Haugland, Dec 22 2001 EXTENSIONS a(31)-a(35) (using data in A018789) from Alois P. Heinz, Sep 08 2019 STATUS approved

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Last modified August 10 16:56 EDT 2020. Contains 336381 sequences. (Running on oeis4.)