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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 (list; graph; refs; listen; history; text; internal format)
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), 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.

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)/(1-x). (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

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Last modified December 9 00:32 EST 2019. Contains 329871 sequences. (Running on oeis4.)