The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A317245 Number of supernormal integer partitions of n. 27
 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, 12, 18, 17, 21, 19, 28, 23, 28, 26, 27, 24, 32, 29, 36, 34, 46, 42, 55, 48, 65, 65, 74, 70, 88, 81, 83, 103, 112, 129, 153, 157, 190, 205, 210, 242, 283, 276, 321 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS 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. LINKS EXAMPLE The a(10) = 4 supernormal integer partitions are (4321), (33211), (322111), (1111111111). The a(21) = 10 supernormal integer partitions:   (654321),   (4443321),   (44432211), (44333211), (44332221),   (4432221111), (4333221111), (4332222111),   (433322211),   (111111111111111111111). MATHEMATICA supnrm[q_]:=Or[q=={}||Union[q]=={1}, And[Union[q]==Range[Max[q]], supnrm[Sort[Length/@Split[q], Greater]]]]; Table[Length[Select[IntegerPartitions[n], supnrm]], {n, 0, 30}] CROSSREFS Cf. A000041, A181819, A182850, A182857, A275870, A304660, A305563, A317081, A317086, A317088, A317246. Sequence in context: A086394 A029226 A093354 * A332277 A109701 A124751 Adjacent sequences:  A317242 A317243 A317244 * A317246 A317247 A317248 KEYWORD nonn AUTHOR Gus Wiseman, Jul 24 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 14 03:00 EDT 2021. Contains 343872 sequences. (Running on oeis4.)