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 A018789 Number of subsets of { 1, ..., n } containing an arithmetic progression of length 4. 2
 0, 0, 0, 0, 1, 3, 8, 25, 64, 148, 356, 826, 1863, 4205, 9246, 19865, 42935, 90872, 190561, 399104, 829883, 1710609, 3523315, 7224223, 14755538, 30092167, 61177910, 124028647, 251168840, 507216174, 1022829206, 2061466047, 4149639752 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS Sean A. Irvine, Table of n, a(n) for n = 0..39 FORMULA a(n) = 2^n - A066369(n). EXAMPLE In {1,2,3,4,5} the only length 4 progressions possible are 1,2,3,4 and 2,3,4,5. There are three sets containing one or more of these: {1,2,3,4},{2,3,4,5}, and {1,2,3,4,5}. Thus a(5) = 3. - David Nacin, Mar 05 2012 PROG (Python) from itertools import combinations # Prints out all such sets def containsap4(n): ap4list = list() for skip in range(1, (n + 2) // 3): for start in range(1, n + 1 - 3 * skip): ap4list.append( set({start, start + skip, start + 2 * skip, start + 3 * skip}) ) s = list() for i in range(4, n + 1): for temptuple in combinations(range(1, n + 1), i): tempset = set(temptuple) for sub in ap4list: if sub <= tempset: s.append(tempset) break return s # Counts all such sets def a(n): return len(containsap4(n)) # David Nacin, Mar 05 2012 for n in range(20): print(a(n), end=", ") CROSSREFS Cf. A066369. Sequence in context: A026980 A026955 A093900 * A203413 A301604 A141799 Adjacent sequences: A018786 A018787 A018788 * A018790 A018791 A018792 KEYWORD nonn AUTHOR David W. Wilson STATUS approved

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Last modified September 18 11:08 EDT 2024. Contains 375999 sequences. (Running on oeis4.)