OFFSET
0,6
COMMENTS
Each quotient of adjacent parts is between 1/2 and 2 exclusive.
LINKS
Bert Dobbelaere, Table of n, a(n) for n = 0..100
EXAMPLE
The a(1) = 1 through a(17) = 17 compositions (A..G = 10..16):
1 2 3 4 5 6 7 8 9 A B C D E F G
23 34 35 45 46 47 57 58 59 69 6A
32 43 53 54 64 56 75 67 68 78 79
234 235 65 345 76 86 87 97
432 532 74 354 85 95 96 A6
435 346 347 357 358
453 643 356 456 457
534 653 465 475
543 743 546 547
2345 564 574
2354 645 745
4532 654 754
5432 753 853
2346 2347
6432 2356
6532
7432
MATHEMATICA
Table[Length[Select[Join@@Permutations/@Select[IntegerPartitions[n], UnsameQ@@#&], And@@Table[#[[i]]<2*#[[i-1]]&&#[[i-1]]<2*#[[i]], {i, 2, Length[#]}]&]], {n, 0, 15}]
CROSSREFS
The non-strict version is A342330.
A000929 counts partitions with adjacent parts x >= 2y.
A002843 counts compositions with adjacent parts x <= 2y.
A154402 counts partitions with adjacent parts x = 2y.
A274199 counts compositions with adjacent parts x < 2y.
A342098 counts partitions with adjacent parts x > 2y.
A342331 counts compositions with adjacent parts x = 2y or y = 2x.
A342332 counts compositions with adjacent parts x > 2y or y > 2x.
A342333 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.
A342338 counts compositions with adjacent parts x < 2y and y <= 2x.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 12 2021
EXTENSIONS
More terms from Bert Dobbelaere, Mar 19 2021
STATUS
approved