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 A049986 #63 Aug 12 2024 09:34:57
%S A049986 0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,1,0,1,0,2,1,2,0,1,2,2,1,3,0,4,0,2,1,3,
%T A049986 4,4,0,3,1,6,0,5,0,4,6,4,0,4,2,8,2,5,0,6,6,6,2,5,0,11,0,5,5,6,7,8,0,6,
%U A049986 2,15,0,9,0,6,10,7,4,9,0,14,5,7,0,12,9,7,3
%N A049986 a(n) is the number of arithmetic progressions of 4 or more positive integers, strictly increasing with sum n.
%H A049986 Antti Karttunen, <a href="/A049986/b049986.txt">Table of n, a(n) for n = 1..12580</a>
%H A049986 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 A049986 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 A049986 Jon Maiga, <a href="http://sequencedb.net/s/A049986">Computer-generated formulas for A049986</a>, Sequence Machine.
%H A049986 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 A049986 Graeme McRae, <a href="/A049988/a049988.pdf">Counting arithmetic sequences whose sum is n</a> [Cached copy]
%H A049986 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 A049986 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 A049986 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.
%F A049986 G.f.: Sum_{k >= 4} x^t(k)/(x^t(k) - x^t(k-1) - x^k + 1) = Sum_{k >= 4} x^t(k)/((1 - x^k)*(1 - x^t(k-1))), where t(k) = k*(k+1)/2 = A000217(k) is the k-th triangular number [_Graeme McRae_]. - _Petros Hadjicostas_, Sep 29 2019
%F A049986 a(n) = A049994(n) - A321014(n). [Listed by Sequence Machine and obviously true] - _Antti Karttunen_, Feb 20 2023
%o A049986 (PARI)
%o A049986 \\ Needs also code from A014405 and A023645:
%o A049986 A049994(n) = (A014405(n) + A023645(n) - if(n%3, 0, n/3));
%o A049986 A321014(n) = (numdiv(n) - 3 + !!(n%2) + !!(n%3)); \\ From A321014.
%o A049986 A049986(n) = (A049994(n)-A321014(n)); \\ _Antti Karttunen_, Feb 20 2023
%Y A049986 Cf. A014405, A014406, A049980, A049981, A049982, A049983, A049987 (partial sums), A049988, A049989, A049990, A049991, A049994, A127938, A321014.
%K A049986 nonn
%O A049986 1,20
%A A049986 _Clark Kimberling_