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%I #37 Sep 30 2019 03:15:28
%S 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,
%T 23,25,26,29,33,37,37,40,41,47,47,52,52,56,62,66,66,70,72,80,82,87,87,
%U 93,99,105,107,112,112,123,123,128,133,139,146,154,154,160,162,177,177,186,186,192,202
%N a(n) is the number of arithmetic progressions of 4 or more positive integers, strictly increasing 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="https://eudml.org/doc/228820">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.
%F From _Petros Hadjicostas_, Sep 29 2019: (Start)
%F a(n) = Sum_{k = 1..n} A049986(k).
%F G.f.: (g.f. of A049986)/(1-x). (End)
%Y Cf. A014405, A014406, A049980, A049981, A049982, A049983, A049986, A049987, A049988, A049989, A049990, A127938.
%K nonn
%O 1,14
%A _Clark Kimberling_
%E More terms from _Petros Hadjicostas_, Sep 29 2019
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