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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
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..450
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.
Sequence in context: A320347 A178932 A325852 * A206439 A097450 A062303
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 28 2020
STATUS
approved