A049995 - OEIS

%I #34 Sep 30 2019 01:37:31

%S 0,0,0,1,2,3,4,6,7,10,11,14,15,18,21,25,26,30,31,37,40,44,45,51,55,59,

%T 62,69,70,79,80,86,89,94,101,111,112,117,120,132,133,143,144,152,162,

%U 168,169,180,184,196,200,209,210,221,230,242,246,253,254,274,275,282,291,302,312,325,326,336

%N Number of arithmetic progressions of 4 or more positive integers, nondecreasing with sum <= n.

%H Sadek Bouroubi and Nevrine 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="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 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 From _Petros Hadjicostas_, Sep 29 2019: (Start)

%F a(n) = Sum_{k = 1..n} A049994(k).

%F G.f.: (g.f. of A049994)/(1-x). (End)

%Y Cf. A014405, A014406, A049980, A049981, A049982, A049983, A049987, A049988, A049989, A049990, A049991, A049992, A049993, A049994, A127938.

%K nonn

%O 1,5

%A _Clark Kimberling_

%E More terms from _Petros Hadjicostas_, Sep 29 2019