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A049995
Number of arithmetic progressions of 4 or more positive integers, nondecreasing with sum <= n.
0
0, 0, 0, 1, 2, 3, 4, 6, 7, 10, 11, 14, 15, 18, 21, 25, 26, 30, 31, 37, 40, 44, 45, 51, 55, 59, 62, 69, 70, 79, 80, 86, 89, 94, 101, 111, 112, 117, 120, 132, 133, 143, 144, 152, 162, 168, 169, 180, 184, 196, 200, 209, 210, 221, 230, 242, 246, 253, 254, 274, 275, 282, 291, 302, 312, 325, 326, 336
OFFSET
1,5
LINKS
Sadek Bouroubi and Nevrine 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.
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} A049994(k).
G.f.: (g.f. of A049994)/(1-x). (End)
KEYWORD
nonn
EXTENSIONS
More terms from Petros Hadjicostas, Sep 29 2019
STATUS
approved