A049987 a(n) is the number of arithmetic progressions of 4 or more positive integers, strictly increasing with sum <= n.
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 3, 4, 4, 5, 5, 7, 8, 10, 10, 11, 13, 15, 16, 19, 19, 23, 23, 25, 26, 29, 33, 37, 37, 40, 41, 47, 47, 52, 52, 56, 62, 66, 66, 70, 72, 80, 82, 87, 87, 93, 99, 105, 107, 112, 112, 123, 123, 128, 133, 139, 146, 154, 154, 160, 162, 177, 177, 186, 186, 192, 202
Offset: 1
Keywords
Links
- Sadek Bouroubi and Nesrine Benyahia Tani, Integer partitions into arithmetic progressions, Rostok. Math. Kolloq. 64 (2009), 11-16.
- Sadek Bouroubi and Nesrine Benyahia Tani, Integer partitions into arithmetic progressions with an odd common difference, Integers 9(1) (2009), 77-81.
- Graeme McRae, Counting arithmetic sequences whose sum is n.
- Graeme McRae, Counting arithmetic sequences whose sum is n [Cached copy]
- Augustine O. Munagi, Combinatorics of integer partitions in arithmetic progression, Integers 10(1) (2010), 73-82.
- Augustine O. Munagi and Temba Shonhiwa, On the partitions of a number into arithmetic progressions, Journal of Integer Sequences 11 (2008), Article 08.5.4.
Crossrefs
Formula
From Petros Hadjicostas, Sep 29 2019: (Start)
a(n) = Sum_{k = 1..n} A049986(k).
G.f.: (g.f. of A049986)/(1-x). (End)
Extensions
More terms from Petros Hadjicostas, Sep 29 2019