A317245 - OEIS

A317245

Number of supernormal integer partitions of n.

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

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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

Table of n, a(n) for n=0..68.

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