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%I #40 Sep 30 2019 01:37:59
%S 0,0,1,2,3,6,7,9,13,16,17,24,25,28,36,40,41,51,52,58,68,72,73,87,91,
%T 95,107,114,115,134,135,141,155,160,167,189,190,195,211,223,224,248,
%U 249,257,282,288,289,316,320,332,353,362,363,392,401,413,436,443,444,484,485,492,522,533,543,578
%N a(n) is the number of arithmetic progressions of 3 or more positive integers, nondecreasing with sum <= n.
%H Sadek Bouroubi and Nesrine Benyahia Tani, <a href="http://ftp.math.uni-rostock.de/pub/romako/heft64/bou64.pdf">Integer partitions into arithmetic progressions</a>, Rostok. Math. Kolloq. 64 (2009), 11-16.
%H Sadek Bouroubi and Nesrine Benyahia Tani, <a href="https://www.emis.de/journals/INTEGERS/papers/j7/j7.Abstract.html">Integer partitions into arithmetic progressions with an odd common difference</a>, Integers 9(1) (2009), 77-81.
%H Graeme McRae, <a href="https://web.archive.org/web/20081122034835/http://2000clicks.com/MathHelp/BasicSequenceA049982.htm">Counting arithmetic sequences whose sum is n</a>.
%H Graeme McRae, <a href="/A049988/a049988.pdf">Counting arithmetic sequences whose sum is n</a> [Cached copy]
%H Augustine O. Munagi, <a href="http://www.emis.de/journals/INTEGERS/papers/k7/k7.Abstract.html">Combinatorics of integer partitions in arithmetic progression</a>, Integers 10(1) (2010), 73-82.
%H Augustine O. Munagi and Temba Shonhiwa, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL11/Shonhiwa/shonhiwa13.html">On the partitions of a number into arithmetic progressions</a>, Journal of Integer Sequences 11 (2008), Article 08.5.4.
%H A. N. Pacheco Pulido, <a href="http://www.bdigital.unal.edu.co/7753/">Extensiones lineales de un poset y composiciones de números multipartitos</a>, Maestría thesis, Universidad Nacional de Colombia, 2012.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Arithmetic_progression">Arithmetic progression</a>.
%F From _Petros Hadjicostas_, Sep 29 2019: (Start)
%F a(n) = Sum_{k = 1..n} A049992(k).
%F G.f.: (g.f. of A049992)/(1-x). (End)
%Y Cf. A007862, A014405, A014406, A049980, A049981, A049982, A049983, A049986, A049987, A049988, A049989, A049990, A049991, A049992, A240026, A240027, A307824, A320466, A325325.
%K nonn
%O 1,4
%A _Clark Kimberling_
%E More terms from _Petros Hadjicostas_, Sep 29 2019
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