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

0,3

Links

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..300

Index entries related to non-averaging sequences

Example

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].

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 *)

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.

Sequence in context: A373219 A062436 A342514 * A325874 A293957 A238687

Adjacent sequences: A238568 A238569 A238570 * A238572 A238573 A238574

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Feb 28 2014

Status

approved