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
EXAMPLE
The a(1) = 1 through a(8) = 19 compositions:
(1) (2) (3) (4) (5) (6) (7) (8)
(11) (12) (13) (14) (15) (16) (17)
(21) (22) (23) (24) (25) (26)
(31) (32) (33) (34) (35)
(121) (41) (42) (43) (44)
(122) (51) (52) (53)
(131) (132) (61) (62)
(221) (141) (133) (71)
(231) (142) (134)
(1221) (151) (143)
(232) (152)
(241) (161)
(331) (233)
(242)
(251)
(332)
(341)
(431)
(1331)
MAPLE
b:= proc(n, l, d) option remember; `if`(n=0, 1, add(`if`(l=0 or
j-l<d, b(n-j, j, `if`(l=0, infinity, j-l)), 0), j=1..n))
end:
a:= n-> b(n, 0$2):
seq(a(n), n=0..52); # Alois P. Heinz, Jan 27 2024
MATHEMATICA
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], Greater@@Differences[#]&]], {n, 0, 15}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 10 2019
EXTENSIONS
a(26)-a(44) from Lars Blomberg, May 30 2019
a(45)-a(52) from Alois P. Heinz, Jan 27 2024
STATUS
approved