A049987 a(n) is the number of arithmetic progressions of 4 or more positive integers, strictly increasing with sum <= n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 3, 4, 4, 5, 5, 7, 8, 10, 10, 11, 13, 15, 16, 19, 19, 23, 23, 25, 26, 29, 33, 37, 37, 40, 41, 47, 47, 52, 52, 56, 62, 66, 66, 70, 72, 80, 82, 87, 87, 93, 99, 105, 107, 112, 112, 123, 123, 128, 133, 139, 146, 154, 154, 160, 162, 177, 177, 186, 186, 192, 202

Offset

1,14

Links

Table of n, a(n) for n=1..75.

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.

Formula

From Petros Hadjicostas, Sep 29 2019: (Start)

a(n) = Sum_{k = 1..n} A049986(k).

G.f.: (g.f. of A049986)/(1-x). (End)

Crossrefs

Cf. A014405, A014406, A049980, A049981, A049982, A049983, A049986, A049987, A049988, A049989, A049990, A127938.

Sequence in context: A046700 A216411 A110532 * A343397 A270832 A257646

Adjacent sequences: A049984 A049985 A049986 * A049988 A049989 A049990

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Petros Hadjicostas, Sep 29 2019

Status

approved