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A342341
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Number of strict compositions of n with all adjacent parts (x, y) satisfying x < 2y and y < 2x.
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14
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1, 1, 1, 1, 1, 3, 1, 3, 3, 5, 5, 5, 9, 7, 13, 15, 17, 19, 29, 31, 39, 43, 63, 59, 75, 121, 119, 169, 167, 199, 279, 305, 343, 479, 537, 733, 789, 883, 1057, 1421, 1545, 1831, 2409, 2577, 3343, 4001, 4657, 5131, 6065, 7755, 8841, 10473, 12995, 14659, 17671, 20619, 25157, 28255, 33131, 38265, 47699, 53171, 62611, 80005, 88519, 105937, 119989
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OFFSET
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0,6
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COMMENTS
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Each quotient of adjacent parts is between 1/2 and 2 exclusive.
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LINKS
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EXAMPLE
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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
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MATHEMATICA
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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}]
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CROSSREFS
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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.
Cf. A003114, A003242, A034296, A167606, A342083, A342084, A342087, A342191, A342334, A342336, A342339, A342340.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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