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%I #44 Feb 20 2023 07:51:14
%S 0,0,1,1,1,3,1,2,4,3,1,7,1,3,8,4,1,10,1,6,10,4,1,14,4,4,12,7,1,19,1,6,
%T 14,5,7,22,1,5,16,12,1,24,1,8,25,6,1,27,4,12,21,9,1,29,9,12,23,7,1,40,
%U 1,7,30,11,10,35,1,10,27,21,1,42,1,8,39,11,7,40,1,22,35,9,1,49,12,9,34
%N a(n) is the number of arithmetic progressions of 3 or more positive integers, nondecreasing with sum n.
%H Antti Karttunen, <a href="/A049992/b049992.txt">Table of n, a(n) for n = 1..12580</a>
%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 Jon Maiga, <a href="http://sequencedb.net/s/A049992">Computer-generated formulas for A049992</a>, Sequence Machine.
%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 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 G.f.: Sum_{k>=3} x^k/(1-x^(k*(k-1)/2))/(1-x^k). [_Leroy Quet_ from A049988] - _Petros Hadjicostas_, Sep 29 2019
%F a(n) = A014405(n) + A023645(n) = A049994(n) + A175676(n). [Two of the formulas listed by Sequence Machine, both obviously true] - _Antti Karttunen_, Feb 20 2023
%o (PARI) A049992(n) = (A014405(n)+A023645(n)); \\ (Uses the programs given in A014405 and A023645) - _Antti Karttunen_, Feb 20 2023
%Y Cf. A007862, A014405, A023645, A049980, A049981, A049982, A049983, A049986, A049987, A049988, A049989, A049990, A049991, A049992, A049994, A175676, A240026, A240027, A307824, A320466.
%K nonn
%O 1,6
%A _Clark Kimberling_
%E More terms from _Petros Hadjicostas_, Sep 29 2019
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