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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. 17
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

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. A000079, A049988, A070211, 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 July 20 05:43 EDT 2019. Contains 325168 sequences. (Running on oeis4.)