A049989 a(n) is the number of arithmetic progressions of positive integers, nondecreasing with sum <= n.
1, 3, 6, 10, 14, 21, 26, 33, 42, 51, 58, 72, 80, 91, 107, 120, 130, 150, 161, 178, 199, 215, 228, 255, 272, 290, 316, 338, 354, 389, 406, 429, 460, 483, 508, 549, 569, 594, 630, 663, 685, 731, 754, 785, 833, 863, 888, 940, 969, 1007, 1054, 1090, 1118, 1175, 1212, 1253, 1305, 1342, 1373, 1444, 1476, 1515, 1577, 1621
Offset: 1
Keywords
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..10000
- 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.
- Wikipedia, Arithmetic progression.
- Gus Wiseman, Sequences counting and ranking integer partitions by the differences of their successive parts.
Crossrefs
Programs
-
PARI
seq(n)={my(w=(sqrtint(8*n+1)-1)\2+1); Vec(x/(1-x)^2 + sum(k=2, n, x^k/(1 - if(k<=w, x^(k*(k-1)/2)))/(1-x^k) + O(x*x^n))/(1-x))} \\ Andrew Howroyd, Sep 28 2019
Formula
From Petros Hadjicostas, Sep 29 2019: (Start)
G.f.: (-1 + g.f. of A049988)/(1-x). (End)
Extensions
More terms from Petros Hadjicostas, Sep 28 2019