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A330937
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Number of strictly recursively normal integer partitions of n.
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1
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1, 2, 3, 5, 7, 10, 15, 20, 27, 35, 49, 58, 81, 100, 126, 160, 206, 246, 316, 374, 462, 564, 696, 813, 1006, 1195, 1441, 1701, 2058, 2394, 2896, 3367, 4007, 4670, 5542, 6368, 7540, 8702, 10199, 11734, 13760, 15734, 18384, 21008, 24441, 27893, 32380, 36841
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OFFSET
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0,2
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COMMENTS
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A sequence is strictly recursively normal if either it empty, its run-lengths are distinct (strict), or its run-lengths cover an initial interval of positive integers (normal) and are themselves a strictly recursively normal sequence.
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LINKS
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EXAMPLE
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The a(1) = 1 through a(9) = 15 partitions:
(1) (2) (3) (4) (5) (6) (7) (8) (9)
(21) (31) (32) (42) (43) (53) (54)
(211) (41) (51) (52) (62) (63)
(221) (321) (61) (71) (72)
(311) (411) (322) (332) (81)
(331) (422) (432)
(421) (431) (441)
(511) (521) (522)
(3211) (611) (531)
(3221) (621)
(4211) (711)
(3321)
(4221)
(4311)
(5211)
(32211)
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MATHEMATICA
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normQ[m_]:=m=={}||Union[m]==Range[Max[m]];
recnQ[ptn_]:=With[{qtn=Length/@Split[ptn]}, Or[ptn=={}, UnsameQ@@qtn, And[normQ[qtn], recnQ[qtn]]]];
Table[Length[Select[IntegerPartitions[n], recnQ]], {n, 0, 30}]
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CROSSREFS
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The narrow instead of strict version is A332272.
A wide instead of strict version is A332295(n) - 1 for n > 1.
Cf. A107429, A181819, A316496, A317081, A317245, A317491, A329744, A329746, A329766, A332277, A332576.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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