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A238571 Number of partitions of n avoiding any 3-term arithmetic progression. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..300
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: A266745 A062436 A342514 * A325874 A293957 A238687
KEYWORD
nonn
AUTHOR
Joerg Arndt and Alois P. Heinz, Feb 28 2014
STATUS
approved

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Last modified March 28 10:31 EDT 2024. Contains 371240 sequences. (Running on oeis4.)