A049981 a(n) is the number of arithmetic progressions of positive integers, strictly increasing with sum <= n.

1, 2, 4, 6, 9, 13, 17, 21, 28, 34, 40, 49, 56, 64, 77, 86, 95, 110, 120, 132, 150, 163, 175, 195, 210, 225, 248, 265, 280, 308, 324, 342, 370, 390, 412, 445, 464, 486, 519, 545, 566, 605, 627, 653, 696, 723, 747, 790, 817, 850, 894, 925, 952, 1002, 1036, 1070, 1119, 1153, 1183, 1243, 1274, 1310

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

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.
• A. N. Pacheco Pulido, Extensiones lineales de un poset y composiciones de números multipartitos, Maestría thesis, Universidad Nacional de Colombia, 2012.

Crossrefs

Cf. A014405, A014406, A049980, A049982, A049983, A049986, A049987, A068322, A068323, A068324, A127938, A175342.

Formula

From Petros Hadjicostas, Sep 29 2019: (Start)

a(n) = Sum_{k = 1..n} A049980(k) = n + Sum_{k = 1..n} A049982(k).

G.f.: (g.f. of A049980)/(1-x). (End)

Extensions

More terms from Petros Hadjicostas, Sep 29 2019