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A333191
Number of compositions of n whose run-lengths are either strictly increasing or strictly decreasing.
8
1, 1, 2, 2, 5, 8, 10, 18, 24, 29, 44, 60, 68, 100, 130, 148, 201, 256, 310, 396, 478, 582, 736, 898, 1068, 1301, 1594, 1902, 2288, 2750, 3262, 3910, 4638, 5510, 6538, 7686, 9069, 10670, 12560, 14728, 17170, 20090, 23462, 27292, 31710, 36878, 42704, 49430
OFFSET
0,3
COMMENTS
A composition of n is a finite sequence of positive integers summing to n.
LINKS
FORMULA
a(n > 0) = 2*A333192(n) - A000005(n).
EXAMPLE
The a(1) = 1 through a(7) = 18 compositions:
(1) (2) (3) (4) (5) (6) (7)
(11) (111) (22) (113) (33) (115)
(112) (122) (114) (133)
(211) (221) (222) (223)
(1111) (311) (411) (322)
(1112) (1113) (331)
(2111) (3111) (511)
(11111) (11112) (1114)
(21111) (1222)
(111111) (2221)
(4111)
(11113)
(11122)
(22111)
(31111)
(111112)
(211111)
(1111111)
MATHEMATICA
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], Or[Less@@Length/@Split[#], Greater@@Length/@Split[#]]&]], {n, 0, 15}]
CROSSREFS
The non-strict version is A332835.
The case of partitions is A333190.
Unimodal compositions are A001523.
Strict compositions are A032020.
Partitions with distinct run-lengths are A098859.
Partitions with strictly increasing run-lengths are A100471.
Partitions with strictly decreasing run-lengths are A100881.
Partitions with weakly decreasing run-lengths are A100882.
Partitions with weakly increasing run-lengths are A100883.
Compositions with equal run-lengths are A329738.
Compositions whose run-lengths are unimodal are A332726.
Compositions whose run-lengths are unimodal or co-unimodal are A332746.
Compositions whose run-lengths are neither incr. nor decr. are A332833.
Compositions that are neither increasing nor decreasing are A332834.
Compositions with weakly increasing run-lengths are A332836.
Compositions that are strictly incr. or strictly decr. are A333147.
Compositions with strictly increasing run-lengths are A333192.
Sequence in context: A035570 A286559 A183928 * A329739 A126291 A056224
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 17 2020
EXTENSIONS
Terms a(26) and beyond from Giovanni Resta, May 19 2020
STATUS
approved