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 A051013 Number of nonaveraging sequences on {1,2,...,n}. 6
 1, 2, 4, 7, 13, 23, 40, 65, 106, 169, 278, 443, 705, 1117, 1760, 2692, 4151, 6314, 9526, 14127, 20944, 30848, 45589, 66495, 96847, 140840, 204380, 293822, 425859, 613446, 880288, 1258349, 1794256, 2545965, 3623774, 5123746, 7207773, 10159163, 14273328, 19925242, 27893419 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Eric Weisstein's World of Mathematics, Nonaveraging Sequence Wikipedia, Salem-Spencer set FORMULA a(n) = 2^n - A018788(n). - David Nacin, Mar 03 2012 EXAMPLE The only subset of s = {1,2,3} that contains a 3-term arithmetic progression is s itself, so a(3) = 7. MATHEMATICA a[n_] := a[n] = 2^n - Count[Subsets[Range[n], {3, n}], {___, a_, ___, b_, ___, c_, ___} /; b-a == c-b]; Table[Print[n, " ", a[n]]; a[n], {n, 0, 32}] (* Jean-François Alcover, May 30 2019 *) PROG (Python) #Prints out all such sets def nonaveragingsets(n): .avoid=list() .for skip in range(1, (n+1)//2): ..for start in range (1, n+1-2*skip): ...avoid.append(set({start, start+skip, start+2*skip})) .s=list() .for i in range(3): ..for smallset in comb(range(1, n+1), i): ...s.append(smallset) .for i in range(3, 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(nonaveragingsets(n)) # David Nacin, Mar 03 2012 CROSSREFS Cf. A018788. Row sums of A334187. Sequence in context: A001036 A054150 A130709 * A128609 A335471 A168043 Adjacent sequences:  A051010 A051011 A051012 * A051014 A051015 A051016 KEYWORD nonn AUTHOR EXTENSIONS More terms from John W. Layman, Nov 27 2001 a(29)-a(37) from Donovan Johnson, Aug 15 2010 a(38)-a(40) from Alois P. Heinz, Oct 27 2011 STATUS approved

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Last modified September 26 23:32 EDT 2020. Contains 337378 sequences. (Running on oeis4.)