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 A175342 #29 Sep 29 2019 02:05:34
%S A175342 1,2,4,5,6,10,8,10,15,14,12,22,14,18,28,21,18,34,20,28,38,28,24,46,31,
%T A175342 32,48,38,30,62,32,40,58,42,46,73,38,46,68,58,42,84,44,56,90,56,48,94,
%U A175342 55,70,90,66,54,106,70,74,100,70,60,130,62,74,118,81,82,130,68,84,120
%N A175342 Number of arithmetic progressions (where the difference between adjacent terms is either positive, 0, or negative) of positive integers that sum to n.
%H A175342 Lars Blomberg, <a href="/A175342/b175342.txt">Table of n, a(n) for n = 1..10000</a>
%H A175342 Lars Blomberg, <a href="/A175342/a175342.cs.txt">C# program for calculating b-file</a>.
%H A175342 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 A175342 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 A175342 Graeme McRae, <a href="/A049988/a049988.pdf">Counting arithmetic sequences whose sum is n</a> [Cached copy]
%H A175342 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 A175342 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 A175342 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 A175342 Wikipedia, <a href="https://en.wikipedia.org/wiki/Arithmetic_progression">Arithmetic progression</a>.
%H A175342 Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts</a>.
%F A175342 a(n) = 2*A049988(n) - A000005(n).
%F A175342 G.f.: x/(1-x) + Sum_{k>=2} x^k * (1 + x^(k(k-1)/2)) / (1 - x^(k(k-1)/2)) / (1 -x^k).
%e A175342 From _Gus Wiseman_, May 15 2019: (Start)
%e A175342 The a(1) = 1 through a(8) = 10 compositions with equal differences:
%e A175342 (1) (2) (3) (4) (5) (6) (7) (8)
%e A175342 (11) (12) (13) (14) (15) (16) (17)
%e A175342 (21) (22) (23) (24) (25) (26)
%e A175342 (111) (31) (32) (33) (34) (35)
%e A175342 (1111) (41) (42) (43) (44)
%e A175342 (11111) (51) (52) (53)
%e A175342 (123) (61) (62)
%e A175342 (222) (1111111) (71)
%e A175342 (321) (2222)
%e A175342 (111111) (11111111)
%e A175342 (End)
%t A175342 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],SameQ@@Differences[#]&]],{n,0,15}] (* returns a(0) = 1, _Gus Wiseman_, May 15 2019*)
%Y A175342 Cf. A000005, A000079, A049980, A049981, A049982, A049983, A049986, A049987, A049988, A049989, A049990, A070211, A127938, A175327, A325328, A325407, A325545, A325546, A325547, A325548, A325557, A325558.
%K A175342 nonn
%O A175342 1,2
%A A175342 _Leroy Quet_, Apr 17 2010
%E A175342 Edited and extended by _Max Alekseyev_, May 03 2010