A049993 a(n) is the number of arithmetic progressions of 3 or more positive integers, nondecreasing with sum <= n.

0, 0, 1, 2, 3, 6, 7, 9, 13, 16, 17, 24, 25, 28, 36, 40, 41, 51, 52, 58, 68, 72, 73, 87, 91, 95, 107, 114, 115, 134, 135, 141, 155, 160, 167, 189, 190, 195, 211, 223, 224, 248, 249, 257, 282, 288, 289, 316, 320, 332, 353, 362, 363, 392, 401, 413, 436, 443, 444, 484, 485, 492, 522, 533, 543, 578

Offset

1,4

Links

Table of n, a(n) for n=1..66.

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

From Petros Hadjicostas, Sep 29 2019: (Start)

a(n) = Sum_{k = 1..n} A049992(k).

G.f.: (g.f. of A049992)/(1-x). (End)

Crossrefs

Cf. A007862, A014405, A014406, A049980, A049981, A049982, A049983, A049986, A049987, A049988, A049989, A049990, A049991, A049992, A240026, A240027, A307824, A320466, A325325.

Sequence in context: A153348 A246647 A177729 * A167793 A262932 A018423

Adjacent sequences: A049990 A049991 A049992 * A049994 A049995 A049996

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Petros Hadjicostas, Sep 29 2019

Status

approved