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 A014406 Number of strictly increasing arithmetic progressions of positive integers with at least 3 terms and sum <= n. 14
 0, 0, 0, 0, 0, 1, 1, 1, 3, 4, 4, 7, 7, 8, 13, 14, 14, 20, 20, 22, 29, 31, 31, 39, 41, 43, 52, 55, 55, 68, 68, 70, 81, 84, 88, 103, 103, 106, 119, 125, 125, 143, 143, 147, 167, 171, 171, 190, 192, 200, 218, 223, 223, 246, 252, 258, 278, 283, 283, 313, 313, 318, 343, 349, 356, 385, 385 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,9 LINKS Fausto A. C. Cariboni, Table of n, a(n) for n = 1..1000 Sadek Bouroubi and Nesrine Benyahia Tani, Integer partitions into arithmetic progressions, Rostok. Math. Kolloq. 64 (2009), 11-16. Sadek Bouroubi and Nesrine Benyahia Tani, Integer partitions into arithmetic progressions with an odd common difference, Integers 9(1) (2009), 77-81. Graeme McRae, Counting arithmetic sequences whose sum is n. Graeme McRae, Counting arithmetic sequences whose sum is n [Cached copy] Augustine O. Munagi, Combinatorics of integer partitions in arithmetic progression, Integers 10(1) (2010), 73-82. Augustine O. Munagi and Temba Shonhiwa, On the partitions of a number into arithmetic progressions, Journal of Integer Sequences 11 (2008), Article 08.5.4. A. N. Pacheco Pulido, Extensiones lineales de un poset y composiciones de números multipartitos, Maestría thesis, Universidad Nacional de Colombia, 2012. Wikipedia, Arithmetic progression. FORMULA a(n) = Sum_{k=1..n} A014405(k). - Sean A. Irvine, Oct 22 2018 G.f.: (g.f. of A014405)/(1-x). - Petros Hadjicostas, Sep 29 2019 EXAMPLE From Petros Hadjicostas, Sep 29 2019: (Start) a(8) = 1 because we have only the following strictly increasing arithmetic progression of positive integers with at least 3 terms and sum <= 8: 1+2+3. a(9) = 3 because we have the following strictly increasing arithmetic progressions of positive integers with at least 3 terms and sum <= 9: 1+2+3, 1+3+5, and 2+3+4. a(10) = 4 because we have the following strictly increasing arithmetic progressions of positive integers with at least 3 terms and sum <= 10: 1+2+3, 1+3+5, 2+3+4, and 1+2+3+4. (End) CROSSREFS Cf. A007862, A014405, A047966, A049982, A049983, A049986, A049987, A049988, A049989, A049990, A049991, A129654, A240026, A240027, A307824, A320466, A325325, A325328. Sequence in context: A084138 A127141 A272668 * A154426 A231219 A231343 Adjacent sequences:  A014403 A014404 A014405 * A014407 A014408 A014409 KEYWORD nonn AUTHOR EXTENSIONS a(59)-a(67) corrected by Fausto A. C. Cariboni, Oct 02 2018 STATUS approved

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Last modified December 10 20:23 EST 2019. Contains 329909 sequences. (Running on oeis4.)