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A317588 Number of uniformly normal integer partitions of n. 6
1, 1, 2, 3, 4, 3, 6, 3, 5, 6, 7, 5, 8, 5, 7, 10, 7, 6, 12, 7, 12, 14, 10, 11, 18, 11, 13, 16, 18, 15, 35, 16, 26, 24, 27, 26, 47, 33, 44, 48, 58, 48, 76, 63, 81, 79, 98, 94, 123, 109, 135, 131, 148, 140, 162, 149, 152, 162, 166, 175, 202, 191, 221, 232, 233 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

An integer partition is uniformly normal if either (1) it is of the form (x, x, ..., x) for some x > 0, or (2a) it spans an initial interval of positive integers, and (2b) its multiplicities, sorted in weakly decreasing order, are themselves a uniformly normal integer partition.

LINKS

Table of n, a(n) for n=1..65.

A. David Christopher and M. Davamani Christober, Relatively Prime Uniform Partitions, Gen. Math. Notes, Vol. 13, No. 2, December, 2012, pp.1-12.

EXAMPLE

The a(6) = 6 uniformly normal integer partitions are (6), (33), (321), (222), (2211), (111111). Missing from this list are (51), (42), (411), (3111), (21111).

The a(21) = 14 uniformly normal integer partitions (n = 21):

  (n),

  (777),

  (654321),

  (4443321), (3333333),

  (44432211), (44333211), (44332221),

  (4432221111), (4333221111), (4332222111),

  (433322211),

  (22222221111111),

  (111111111111111111111).

MATHEMATICA

uninrmQ[q_]:=Or[q=={}||Length[Union[q]]==1, And[Union[q]==Range[Max[q]], uninrmQ[Sort[Length/@Split[q], Greater]]]];

Table[Length[Select[IntegerPartitions[n], uninrmQ]], {n, 0, 30}]

CROSSREFS

Cf. A181819, A182850, A275870, A317081, A317088, A317246, A317246, A317491, A317589, A317590.

Sequence in context: A152920 A288778 A290139 * A080383 A086369 A337532

Adjacent sequences:  A317585 A317586 A317587 * A317589 A317590 A317591

KEYWORD

nonn

AUTHOR

Gus Wiseman, Aug 01 2018

STATUS

approved

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Last modified December 4 18:08 EST 2021. Contains 349526 sequences. (Running on oeis4.)