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%I #18 Mar 21 2022 08:08:40
%S 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,
%T 120,130,154,177,193,226,262,291,332,375,419,479,543,608,676,765,859,
%U 961,1075,1202,1336,1495,1672,1854,2050,2301,2536,2814,3142,3448,3809
%N Number of strict integer partitions of n without three consecutive parts in arithmetic progression.
%C Also the number of strict integer partitions of n whose first differences are an anti-run, meaning there are no adjacent equal differences.
%H Fausto A. C. Cariboni, <a href="/A332668/b332668.txt">Table of n, a(n) for n = 0..450</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Arithmetic_progression">Arithmetic progression</a>
%e The a(1) = 1 through a(10) = 9 partitions (A = 10):
%e (1) (2) (3) (4) (5) (6) (7) (8) (9) (A)
%e (21) (31) (32) (42) (43) (53) (54) (64)
%e (41) (51) (52) (62) (63) (73)
%e (61) (71) (72) (82)
%e (421) (431) (81) (91)
%e (521) (621) (532)
%e (541)
%e (631)
%e (721)
%t Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&!MatchQ[Differences[#],{___,x_,x_,___}]&]],{n,0,30}]
%Y Anti-run compositions are counted by A003242.
%Y Normal anti-runs of length n + 1 are counted by A005649.
%Y Strict partitions with equal differences are A049980.
%Y Partitions with equal differences are A049988.
%Y The non-strict version is A238424.
%Y The version for permutations is A295370.
%Y Anti-run compositions are ranked by A333489.
%Y Cf. A006560, A007862, A238423, A307824, A325328, A325852, A325874, A333195.
%K nonn
%O 0,4
%A _Gus Wiseman_, Mar 28 2020
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