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!)
 A070211 Number of compositions (ordered partitions) of n that are concave-down sequences. 15
 1, 1, 2, 4, 6, 9, 14, 18, 24, 34, 42, 52, 68, 82, 101, 126, 147, 175, 213, 246, 289, 344, 392, 453, 530, 598, 687, 791, 885, 1007, 1151, 1276, 1438, 1629, 1806, 2018, 2262, 2490, 2775, 3091, 3387, 3754, 4165, 4542, 5011, 5527, 6012, 6600, 7245, 7864, 8614 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Here, a finite sequence is concave if each term (other than the first or last) is at least the average of the two adjacent terms. - Eric M. Schmidt, Sep 29 2013 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). Then a(n) is the number of compositions of n with weakly decreasing differences. - Gus Wiseman, May 15 2019 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..500 EXAMPLE Out of the 8 ordered partitions of 4, only 2+1+1 and 1+1+2 are not concave, so a(4)=6. From Gus Wiseman, May 15 2019: (Start) The a(1) = 1 through a(6) = 14 compositions:   (1)  (2)   (3)    (4)     (5)      (6)        (11)  (12)   (13)    (14)     (15)              (21)   (22)    (23)     (24)              (111)  (31)    (32)     (33)                     (121)   (41)     (42)                     (1111)  (122)    (51)                             (131)    (123)                             (221)    (132)                             (11111)  (141)                                      (222)                                      (231)                                      (321)                                      (1221)                                      (111111) (End) MATHEMATICA Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], GreaterEqual@@Differences[#]&]], {n, 0, 15}] (* Gus Wiseman, May 15 2019 *) PROG (Sage) def A070211(n) : return sum(all(2*p[i] >= p[i-1] + p[i+1] for i in range(1, len(p)-1)) for p in Compositions(n)) # Eric M. Schmidt, Sep 29 2013 CROSSREFS Cf. A000079, A001523 (weakly unimodal compositions), A069916, A175342, A320466, A325361 (concave-down partitions), A325545, A325546 (concave-up compositions), A325547, A325548, A325557. Sequence in context: A198201 A281989 A328423 * A113753 A024457 A117842 Adjacent sequences:  A070208 A070209 A070210 * A070212 A070213 A070214 KEYWORD nice,nonn AUTHOR Pontus von BrÃ¶mssen, May 07 2002 EXTENSIONS Name edited by Gus Wiseman, May 15 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 August 10 08:13 EDT 2020. Contains 336368 sequences. (Running on oeis4.)