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A325548 Number of compositions of n with strictly decreasing differences. 12
1, 1, 2, 3, 5, 8, 10, 13, 19, 23, 29, 38, 46, 55, 69, 80, 96, 115, 132, 154, 183, 207, 238, 276, 314, 356, 405, 455, 513, 579, 647, 724, 809, 897, 998, 1107, 1225, 1350, 1486, 1639, 1805, 1973, 2166, 2374, 2586, 2824, 3084, 3346, 3646, 3964, 4286, 4655, 5047 (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
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
Sequence in context: A186498 A226330 A226329 * A094568 A251607 A219276
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

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Last modified July 20 18:09 EDT 2024. Contains 374459 sequences. (Running on oeis4.)