A366069 The number of lit cells in weakly increasing partitions of n when light shines from the northwest. Here partitions are represented from left to right by columns of cells.

1, 4, 8, 17, 28, 51, 78, 127, 189, 287, 411, 603, 840, 1187, 1628, 2242, 3015, 4076, 5399, 7173, 9390, 12292, 15904, 20585, 26364, 33748, 42856, 54348, 68446, 86101, 107641, 134383, 166912, 206961, 255479, 314872, 386491, 473632, 578389, 705122, 856900, 1039691

Offset

1,2

Comments

See reference below.

References

A. Becher, A. Knopfmacher, and M. E. Mays, Casting light on integer partitions, preprint.

Links

Table of n, a(n) for n=1..42.

Formula

G.f.: P(q) * Sum_{i>=1} (q^i*(1+q^i)/(1-q^i)), where P(q) is the partition g.f. Product_{i>=1} 1/(1-q^i).

Crossrefs

Cf. A000041.

Sequence in context: A213494 A092321 A366157 * A026353 A067773 A301145

Adjacent sequences: A366066 A366067 A366068 * A366070 A366071 A366072

Keyword

nonn

Author

Arnold Knopfmacher, Sep 29 2023

Extensions

More terms from Alois P. Heinz, Sep 29 2023

Status

approved