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A342342
Number of strict compositions of n with all adjacent parts (x, y) satisfying x <= 2y and y <= 2x.
13
1, 1, 1, 3, 1, 3, 5, 5, 3, 11, 9, 11, 17, 15, 29, 39, 31, 39, 65, 57, 107, 127, 149, 155, 187, 265, 293, 419, 523, 571, 781, 763, 941, 1371, 1387, 2125, 2383, 2775, 3243, 4189, 4555, 5349, 7241, 7997, 10591, 13171, 14581, 17213, 20253, 25177, 27701, 34317
OFFSET
0,4
COMMENTS
Each quotient of adjacent parts is between 1/2 and 2 inclusive.
EXAMPLE
The a(1) = 1 through a(12) = 17 strict compositions (A = 10, B = 11, C = 12):
1 2 3 4 5 6 7 8 9 A B C
12 23 24 34 35 36 46 47 48
21 32 42 43 53 45 64 56 57
123 124 54 235 65 75
321 421 63 532 74 84
234 1234 236 246
243 1243 245 345
324 3421 542 354
342 4321 632 435
423 1235 453
432 5321 534
543
642
1236
1245
5421
6321
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 A224957.
The case with strict relations is A342341 (non-strict: 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.
A342094 counts partitions with adjacent x <= 2y (strict: A342095).
A342096 counts partitions without adjacent x >= 2y (strict: A342097).
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.
Sequence in context: A082082 A016646 A345943 * A182600 A371928 A179760
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 12 2021
EXTENSIONS
a(40)-a(51) from Alois P. Heinz, May 24 2021
STATUS
approved