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%I #6 Jul 24 2018 21:21:50
%S 1,1,1,2,2,2,2,2,2,3,4,4,1,3,3,4,2,4,5,6,6,10,7,10,9,9,10,11,12,12,21,
%T 12,18,17,21,19,28,23,28,26,27,24,32,29,36,34,46,42,55,48,65,65,74,70,
%U 88,81,83,103,112,129,153,157,190,205,210,242,283,276,321
%N Number of supernormal integer partitions of n.
%C An integer partition is supernormal if either (1) it is of the form 1^n for some n >= 0, or (2a) it spans an initial interval of positive integers, and (2b) its multiplicities, sorted in weakly decreasing order, are themselves a supernormal integer partition.
%e The a(10) = 4 supernormal integer partitions are (4321), (33211), (322111), (1111111111).
%e The a(21) = 10 supernormal integer partitions:
%e (654321),
%e (4443321),
%e (44432211), (44333211), (44332221),
%e (4432221111), (4333221111), (4332222111),
%e (433322211),
%e (111111111111111111111).
%t supnrm[q_]:=Or[q=={}||Union[q]=={1},And[Union[q]==Range[Max[q]],supnrm[Sort[Length/@Split[q],Greater]]]];
%t Table[Length[Select[IntegerPartitions[n],supnrm]],{n,0,30}]
%Y Cf. A000041, A181819, A182850, A182857, A275870, A304660, A305563, A317081, A317086, A317088, A317246.
%K nonn
%O 0,4
%A _Gus Wiseman_, Jul 24 2018
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