

A049981


a(n) is the number of arithmetic progressions of positive integers, strictly increasing with sum <= n.


15



1, 2, 4, 6, 9, 13, 17, 21, 28, 34, 40, 49, 56, 64, 77, 86, 95, 110, 120, 132, 150, 163, 175, 195, 210, 225, 248, 265, 280, 308, 324, 342, 370, 390, 412, 445, 464, 486, 519, 545, 566, 605, 627, 653, 696, 723, 747, 790, 817, 850, 894, 925, 952, 1002, 1036, 1070, 1119, 1153, 1183, 1243, 1274, 1310
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..62.
Sadek Bouroubi and Nesrine Benyahia Tani, Integer partitions into arithmetic progressions, Rostok. Math. Kolloq. 64 (2009), 1116.
Sadek Bouroubi and Nesrine Benyahia Tani, Integer partitions into arithmetic progressions with an odd common difference, Integers 9(1) (2009), 7781.
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), 7382.
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.


FORMULA

From Petros Hadjicostas, Sep 29 2019: (Start)
a(n) = Sum_{k = 1..n} A049980(k) = n + Sum_{k = 1..n} A049982(k).
G.f.: (g.f. of A049980)/(1x). (End)


CROSSREFS

Cf. A014405, A014406, A049980, A049982, A049983, A049986, A049987, A068322, A068323, A068324, A127938, A175342.
Sequence in context: A283525 A038709 A186351 * A194178 A194213 A194209
Adjacent sequences: A049978 A049979 A049980 * A049982 A049983 A049984


KEYWORD

nonn


AUTHOR

Clark Kimberling


EXTENSIONS

More terms from Petros Hadjicostas, Sep 29 2019


STATUS

approved



