OFFSET
1,2
LINKS
Lars Blomberg, Table of n, a(n) for n = 1..10000
Lars Blomberg, C# program for calculating b-file.
Sadek Bouroubi and Nesrine Benyahia Tani, Integer partitions into arithmetic progressions, Rostok. Math. Kolloq. 64 (2009), 11-16.
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
EXAMPLE
From Gus Wiseman, May 15 2019: (Start)
The a(1) = 1 through a(8) = 10 compositions with equal differences:
(1) (2) (3) (4) (5) (6) (7) (8)
(11) (12) (13) (14) (15) (16) (17)
(21) (22) (23) (24) (25) (26)
(111) (31) (32) (33) (34) (35)
(1111) (41) (42) (43) (44)
(11111) (51) (52) (53)
(123) (61) (62)
(222) (1111111) (71)
(321) (2222)
(111111) (11111111)
(End)
MATHEMATICA
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], SameQ@@Differences[#]&]], {n, 0, 15}] (* returns a(0) = 1, Gus Wiseman, May 15 2019*)
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Apr 17 2010
EXTENSIONS
Edited and extended by Max Alekseyev, May 03 2010
STATUS
approved