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 A174085 Number of permutations of length n with no consecutive triples i,...i+r,...i+2r for all positive and negative r, and for all equal spacings d. 3
 1, 1, 2, 4, 18, 72, 396, 2328, 17050, 131764, 1199368, 11379524, 123012492, 1386127700 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Here we count both the sequence 1,2,3 (r=1) as a progression in 1,2,3,0,4,5, (note d=1) and in 1,0,2,4,3,5 (here, d=2). Number of permutations of 1..n with no 2-dimensional arithmetic progression of length 3: that is, no three points (i,p(i)), (j,p(j)) and (k,p(k)) such that j-i = k-j and p(j)-p(i) = p(k)-p(j). - David Bevan, Jun 16 2021 LINKS Table of n, a(n) for n=0..13. FORMULA a(n) >= A003407(n) with equality only for n in {0, 1, 2, 3}. EXAMPLE a(3) = 4; 123 and 321 each contain a 3-term arithmetic progression. Since the only possibilities for progressions for n=4 are d=1 and r=1 and -1, we get the same term as A095816(4). CROSSREFS Cf. A095816, A174084, A174086, A174087. Cf. A179040 (number of permutations of 1..n with no three elements collinear). Cf. A003407 for another interpretation of avoiding 3-term APs. Sequence in context: A007727 A303352 A226011 * A325850 A052689 A139104 Adjacent sequences: A174082 A174083 A174084 * A174086 A174087 A174088 KEYWORD nonn,more AUTHOR Isaac Lambert, Apr 20 2010 EXTENSIONS a(0)-a(3) and a(10)-a(13) from David Bevan, Jun 16 2021 STATUS approved

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Last modified December 9 11:16 EST 2023. Contains 367690 sequences. (Running on oeis4.)