OFFSET
0,3
COMMENTS
These are finite sequences q of positive integers summing to n such that q(i) = q(i+2) for all possible i.
LINKS
EXAMPLE
The a(1) = 1 through a(8) = 16 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) (141) (61) (62)
(11111) (222) (151) (71)
(1212) (232) (161)
(2121) (313) (242)
(111111) (12121) (323)
(1111111) (1313)
(2222)
(3131)
(21212)
(11111111)
MATHEMATICA
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], SameQ@@Plus@@@Reverse/@Partition[#, 2, 1]&]], {n, 0, 15}]
CROSSREFS
The odd-length case is A062968.
The even-length case is A065608.
The version with alternating parts weakly decreasing is A342528.
A000005 counts constant compositions.
A000041 counts weakly increasing (or weakly decreasing) compositions.
A000203 adds up divisors.
A002843 counts compositions with all adjacent parts x <= 2y.
A003242 counts anti-run compositions.
A175342 counts compositions with constant differences.
A342495 counts compositions with constant first quotients.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 24 2021
STATUS
approved