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

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