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 A049989 a(n) is the number of arithmetic progressions of positive integers, nondecreasing with sum <= n. 13
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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. FORMULA From Petros Hadjicostas, Sep 29 2019: (Start) a(n) = Sum_{k = 1..n} A049988(k). [Note that the offset of A049988 is 0.] G.f.: (-1 + g.f. of A049988)/(1-x). (End) PROG (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 CROSSREFS Cf. A047966, A049982, A049983, A049984, A049986, A049987, A129654, A240026, A240027, A307824, A320466, A325325, A325328. Sequence in context: A183863 A140949 A025206 * A330258 A197056 A104619 Adjacent sequences:  A049986 A049987 A049988 * A049990 A049991 A049992 KEYWORD nonn AUTHOR EXTENSIONS More terms from Petros Hadjicostas, Sep 28 2019 STATUS approved

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Last modified October 24 20:35 EDT 2021. Contains 348233 sequences. (Running on oeis4.)