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 A175342 Number of arithmetic progressions (where the difference between adjacent terms is either positive, 0, or negative) of positive integers that sum to n. 43
 1, 2, 4, 5, 6, 10, 8, 10, 15, 14, 12, 22, 14, 18, 28, 21, 18, 34, 20, 28, 38, 28, 24, 46, 31, 32, 48, 38, 30, 62, 32, 40, 58, 42, 46, 73, 38, 46, 68, 58, 42, 84, 44, 56, 90, 56, 48, 94, 55, 70, 90, 66, 54, 106, 70, 74, 100, 70, 60, 130, 62, 74, 118, 81, 82, 130, 68, 84, 120 (list; graph; refs; listen; history; text; internal format)
 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. Gus Wiseman, Sequences counting and ranking integer partitions by the differences of their successive parts. FORMULA a(n) = 2*A049988(n) - A000005(n). G.f.: x/(1-x) + Sum_{k>=2} x^k * (1 + x^(k(k-1)/2)) / (1 - x^(k(k-1)/2)) / (1 -x^k). 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 Cf. A000005, A000079, A049980, A049981, A049982, A049983, A049986, A049987, A049988, A049989, A049990, A070211, A127938, A175327, A325328, A325407, A325545, A325546, A325547, A325548, A325557, A325558. Sequence in context: A136585 A122721 A014224 * A077312 A325558 A140779 Adjacent sequences: A175339 A175340 A175341 * A175343 A175344 A175345 KEYWORD nonn AUTHOR Leroy Quet, Apr 17 2010 EXTENSIONS Edited and extended by Max Alekseyev, May 03 2010 STATUS approved

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Last modified June 1 20:24 EDT 2023. Contains 363078 sequences. (Running on oeis4.)