This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A049989 #44 Sep 30 2019 01:25:18
%S A049989 1,3,6,10,14,21,26,33,42,51,58,72,80,91,107,120,130,150,161,178,199,
%T A049989 215,228,255,272,290,316,338,354,389,406,429,460,483,508,549,569,594,
%U A049989 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
%N A049989 a(n) is the number of arithmetic progressions of positive integers, nondecreasing with sum <= n.
%H A049989 Andrew Howroyd, <a href="/A049989/b049989.txt">Table of n, a(n) for n = 1..10000</a>
%H A049989 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 A049989 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 A049989 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 A049989 Graeme McRae, <a href="/A049988/a049988.pdf">Counting arithmetic sequences whose sum is n</a> [Cached copy]
%H A049989 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 A049989 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 A049989 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 A049989 Wikipedia, <a href="https://en.wikipedia.org/wiki/Arithmetic_progression">Arithmetic progression</a>.
%H A049989 Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts</a>.
%F A049989 From _Petros Hadjicostas_, Sep 29 2019: (Start)
%F A049989 a(n) = Sum_{k = 1..n} A049988(k). [Note that the offset of A049988 is 0.]
%F A049989 G.f.: (-1 + g.f. of A049988)/(1-x). (End)
%o A049989 (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
%Y A049989 Cf. A047966, A049982, A049983, A049984, A049986, A049987, A129654, A240026, A240027, A307824, A320466, A325325, A325328.
%K A049989 nonn
%O A049989 1,2
%A A049989 _Clark Kimberling_
%E A049989 More terms from _Petros Hadjicostas_, Sep 28 2019