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

1, 1, 2, 2, 4, 5, 6, 8, 12, 12, 19, 23, 27, 34, 43, 49, 62, 74, 88, 104, 127, 145, 176, 199, 239, 272, 324, 378, 430, 490, 583, 654, 750, 876, 988, 1112, 1291, 1441, 1642, 1877, 2121, 2358, 2682, 2977, 3365, 3830, 4237, 4734, 5357, 5868, 6590, 7398, 8182, 9049

Offset: 0

Author

Joerg Arndt and Alois P. Heinz, Feb 28 2014

Keywords

• nonn

Examples

			a(3) = 2: [2,1], [3].
a(4) = 4: [2,1,1], [2,2], [3,1], [4].
a(5) = 5: [2,2,1], [3,1,1], [3,2], [4,1], [5].
a(6) = 6: [2,2,1,1], [3,3], [4,1,1], [4,2], [5,1], [6].
a(7) = 8: [3,2,2], [3,3,1], [4,2,1], [4,3], [5,1,1], [5,2], [6,1], [7].
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].
		

Links

• Fausto A. C. Cariboni, Table of n, a(n) for n = 0..300
• Index entries related to non-averaging sequences

Crossrefs

Cf. A003407 (the same for permutations).

Cf. A178932 (the same for strict partitions).

Cf. A238569 (the same for compositions).

Cf. A238433 (partitions avoiding equidistant 3-term arithmetic progressions).

Cf. A238424 (partitions avoiding three consecutive parts in arithmetic progression).

Cf. A238687.

Programs

Mathematica

a[n_] := a[n] = Count[IntegerPartitions[n], P_ /; {} == SequencePosition[P, {_, i_, _, j_, _, k_, _} /; j - i == k - j, 1]];
Table[Print[n, " ", a[n]]; a[n], {n, 0, 50}] (* Jean-François Alcover, Oct 29 2021 *)