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A238571 Number of partitions of n avoiding any 3-term arithmetic progression.

%I A238571 #24 Oct 29 2021 05:05:41
%S A238571 1,1,2,2,4,5,6,8,12,12,19,23,27,34,43,49,62,74,88,104,127,145,176,199,
%T A238571 239,272,324,378,430,490,583,654,750,876,988,1112,1291,1441,1642,1877,
%U A238571 2121,2358,2682,2977,3365,3830,4237,4734,5357,5868,6590,7398,8182,9049
%N A238571 Number of partitions of n avoiding any 3-term arithmetic progression.
%H A238571 Fausto A. C. Cariboni, <a href="/A238571/b238571.txt">Table of n, a(n) for n = 0..300</a>
%H A238571 <a href="/index/No#non_averaging">Index entries related to non-averaging sequences</a>
%e A238571 a(3) = 2: [2,1], [3].
%e A238571 a(4) = 4: [2,1,1], [2,2], [3,1], [4].
%e A238571 a(5) = 5: [2,2,1], [3,1,1], [3,2], [4,1], [5].
%e A238571 a(6) = 6: [2,2,1,1], [3,3], [4,1,1], [4,2], [5,1], [6].
%e A238571 a(7) = 8: [3,2,2], [3,3,1], [4,2,1], [4,3], [5,1,1], [5,2], [6,1], [7].
%e A238571 a(8) = 12: [3,3,1,1], [3,3,2], [4,2,1,1], [4,2,2], [4,3,1], [4,4], [5,2,1], [5,3], [6,1,1], [6,2], [7,1], [8].
%t A238571 a[n_] := a[n] = Count[IntegerPartitions[n], P_ /; {} == SequencePosition[P, {___, i_, ___, j_, ___, k_, ___} /; j - i == k - j, 1]];
%t A238571 Table[Print[n, " ", a[n]]; a[n], {n, 0, 50}] (* _Jean-François Alcover_, Oct 29 2021 *)
%Y A238571 Cf. A003407 (the same for permutations).
%Y A238571 Cf. A178932 (the same for strict partitions).
%Y A238571 Cf. A238569 (the same for compositions).
%Y A238571 Cf. A238433 (partitions avoiding equidistant 3-term arithmetic progressions).
%Y A238571 Cf. A238424 (partitions avoiding three consecutive parts in arithmetic progression).
%Y A238571 Cf. A238687.
%K A238571 nonn
%O A238571 0,3
%A A238571 _Joerg Arndt_ and _Alois P. Heinz_, Feb 28 2014