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
Keywords
References
- A. Becher, A. Knopfmacher, and M. E. Mays, Casting light on integer partitions, preprint.
Crossrefs
Cf. A000041.
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).
Extensions
More terms from Alois P. Heinz, Sep 29 2023
Comments