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A330937 Number of strictly recursively normal integer partitions of n. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=0..47.

EXAMPLE

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)

MATHEMATICA

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}]

CROSSREFS

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.

Sequence in context: A291298 A092021 A022475 * A011972 A272402 A321176

Adjacent sequences:  A330934 A330935 A330936 * A330938 A330939 A330940

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 09 2020

STATUS

approved

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Last modified May 28 16:25 EDT 2020. Contains 334684 sequences. (Running on oeis4.)