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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.
2
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.
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
KEYWORD
nonn
AUTHOR
Arnold Knopfmacher, Sep 29 2023
EXTENSIONS
More terms from Alois P. Heinz, Sep 29 2023
STATUS
approved