OFFSET
0,4
COMMENTS
Also the number of compositions of n with all adjacent parts (x, y) satisfying x > 2y or y >= 2x.
EXAMPLE
The a(1) = 1 through a(8) = 16 compositions:
(1) (2) (3) (4) (5) (6) (7) (8)
(12) (13) (14) (15) (16) (17)
(31) (41) (24) (25) (26)
(131) (51) (52) (62)
(141) (61) (71)
(312) (124) (125)
(151) (152)
(241) (161)
(313) (251)
(412) (314)
(1312) (413)
(512)
(1241)
(1313)
(1412)
(3131)
MATHEMATICA
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], And@@Table[#[[i]]>=2*#[[i-1]]||#[[i-1]]>2*#[[i]], {i, 2, Length[#]}]&]], {n, 0, 15}]
CROSSREFS
The version not allowing equality (i.e., strict relations) is A342332.
The version allowing equality (i.e., non-strict relations) is A342333.
Reversing operators and changing 'or' into 'and' gives A342338.
A002843 counts compositions with adjacent parts x <= 2y.
A154402 counts partitions with adjacent parts x = 2y.
A274199 counts compositions with adjacent parts x < 2y.
A342331 counts compositions with adjacent parts x = 2y or y = 2x.
A342335 counts compositions with adjacent parts x >= 2y or y = 2x.
A342337 counts partitions with adjacent parts x = y or x = 2y.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 10 2021
EXTENSIONS
More terms from Joerg Arndt, Mar 12 2021
STATUS
approved