The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A325557 Number of compositions of n with equal differences up to sign. 20
 1, 1, 2, 4, 6, 8, 13, 12, 20, 24, 25, 29, 49, 40, 50, 64, 86, 80, 105, 102, 164, 175, 186, 208, 325, 316, 382, 476, 624, 660, 814, 961, 1331, 1500, 1739, 2140, 2877, 3274, 3939, 4901, 6345, 7448, 9054, 11157, 14315, 17181, 20769, 25843, 32947, 39639, 48257, 60075 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A composition of n is a finite sequence of positive integers summing to n. The differences of a sequence are defined as if the sequence were increasing, so for example the differences of (3,1,2) are (-2,1). LINKS Andrew Howroyd, Table of n, a(n) for n = 0..200 EXAMPLE The a(1) = 1 through a(8) = 20 compositions:   (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)                     (121)   (41)     (42)      (43)       (44)                     (1111)  (131)    (51)      (52)       (53)                             (212)    (123)     (61)       (62)                             (11111)  (141)     (151)      (71)                                      (222)     (232)      (161)                                      (321)     (313)      (242)                                      (1212)    (12121)    (323)                                      (2121)    (1111111)  (1232)                                      (111111)             (1313)                                                           (2123)                                                           (2222)                                                           (2321)                                                           (3131)                                                           (3212)                                                           (21212)                                                           (11111111) MATHEMATICA Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], SameQ@@Abs[Differences[#]]&]], {n, 0, 15}] PROG (PARI) step(R, n, s)={matrix(n, n, i, j, if(i>j, if(j>s, R[i-j, j-s]) + if(j+s<=n, R[i-j, j+s])) )} w(n, s)={my(R=matid(n), t=0); while(R, R=step(R, n, s); t+=vecsum(R[n, ])); t} a(n) = {numdiv(max(1, n)) + sum(s=1, n-1, w(n, s))} \\ Andrew Howroyd, Aug 22 2019 CROSSREFS Cf. A000079, A047966, A049988, A070211, A098504, A173258, A175342, A325545, A325546, A325547, A325548, A325552, A325558. Sequence in context: A187779 A086141 A067883 * A283769 A338352 A117117 Adjacent sequences:  A325554 A325555 A325556 * A325558 A325559 A325560 KEYWORD nonn AUTHOR Gus Wiseman, May 11 2019 EXTENSIONS a(26)-a(42) from Lars Blomberg, May 30 2019 Terms a(43) and beyond from Andrew Howroyd, Aug 22 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 23 02:41 EDT 2021. Contains 347609 sequences. (Running on oeis4.)