cp's OEIS Frontend

A317245 Number of supernormal integer partitions of n.

%I A317245 #6 Jul 24 2018 21:21:50
%S A317245 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 A317245 12,18,17,21,19,28,23,28,26,27,24,32,29,36,34,46,42,55,48,65,65,74,70,
%U A317245 88,81,83,103,112,129,153,157,190,205,210,242,283,276,321
%N A317245 Number of supernormal integer partitions of n.
%C A317245 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 A317245 The a(10) = 4 supernormal integer partitions are (4321), (33211), (322111), (1111111111).
%e A317245 The a(21) = 10 supernormal integer partitions:
%e A317245   (654321),
%e A317245   (4443321),
%e A317245   (44432211), (44333211), (44332221),
%e A317245   (4432221111), (4333221111), (4332222111),
%e A317245   (433322211),
%e A317245   (111111111111111111111).
%t A317245 supnrm[q_]:=Or[q=={}||Union[q]=={1},And[Union[q]==Range[Max[q]],supnrm[Sort[Length/@Split[q],Greater]]]];
%t A317245 Table[Length[Select[IntegerPartitions[n],supnrm]],{n,0,30}]
%Y A317245 Cf. A000041, A181819, A182850, A182857, A275870, A304660, A305563, A317081, A317086, A317088, A317246.
%K A317245 nonn
%O A317245 0,4
%A A317245 _Gus Wiseman_, Jul 24 2018