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A332668 Number of strict integer partitions of n without three consecutive parts in arithmetic progression. 5
1, 1, 1, 2, 2, 3, 3, 5, 6, 6, 9, 11, 11, 15, 20, 19, 26, 31, 34, 41, 50, 53, 67, 78, 84, 99, 120, 130, 154, 177, 193, 226, 262, 291, 332, 375, 419, 479, 543, 608, 676, 765, 859, 961, 1075, 1202, 1336, 1495, 1672, 1854, 2050, 2301, 2536, 2814, 3142, 3448, 3809 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Also the number of strict integer partitions of n whose first differences are an anti-run, meaning there are no adjacent equal differences.

LINKS

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..400

Wikipedia, Arithmetic progression

EXAMPLE

The a(1) = 1 through a(10) = 9 partitions (A = 10):

  (1)  (2)  (3)   (4)   (5)   (6)   (7)    (8)    (9)    (A)

            (21)  (31)  (32)  (42)  (43)   (53)   (54)   (64)

                        (41)  (51)  (52)   (62)   (63)   (73)

                                    (61)   (71)   (72)   (82)

                                    (421)  (431)  (81)   (91)

                                           (521)  (621)  (532)

                                                         (541)

                                                         (631)

                                                         (721)

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&!MatchQ[Differences[#], {___, x_, x_, ___}]&]], {n, 0, 30}]

CROSSREFS

Anti-run compositions are counted by A003242.

Normal anti-runs of length n + 1 are counted by A005649.

Strict partitions with equal differences are A049980.

Partitions with equal differences are A049988.

The non-strict version is A238424.

The version for permutations is A295370.

Anti-run compositions are ranked by A333489.

Cf. A006560, A007862, A238423, A307824, A325328, A325852, A325874, A333195.

Sequence in context: A320347 A178932 A325852 * A206439 A097450 A062303

Adjacent sequences:  A332665 A332666 A332667 * A332669 A332670 A332671

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 28 2020

STATUS

approved

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Last modified July 25 15:30 EDT 2021. Contains 346291 sequences. (Running on oeis4.)