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A342342
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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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13
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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
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OFFSET
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0,4
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COMMENTS
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Each quotient of adjacent parts is between 1/2 and 2 inclusive.
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LINKS
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EXAMPLE
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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
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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, 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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