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A342097
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Number of strict integer partitions of n with no adjacent parts having quotient >= 2.
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37
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1, 1, 1, 1, 2, 1, 2, 2, 3, 3, 3, 3, 4, 6, 6, 7, 8, 8, 9, 11, 13, 15, 18, 20, 24, 25, 29, 32, 39, 42, 48, 54, 63, 72, 81, 89, 102, 116, 132, 147, 165, 187, 210, 238, 264, 296, 329, 371, 414, 465, 516, 580, 644, 722, 803, 897, 994, 1108, 1229, 1367, 1512, 1678
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OFFSET
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1,5
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COMMENTS
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The decapitation of such a partition (delete the greatest part) is term-wise greater than its negated first-differences.
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LINKS
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EXAMPLE
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The a(1) = 1 through a(16) = 7 partitions (A..G = 10..16):
1 2 3 4 5 6 7 8 9 A B C D E F G
32 43 53 54 64 65 75 76 86 87 97
432 532 74 543 85 95 96 A6
643 653 654 754
743 753 853
5432 6432 6532
7432
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&And@@Thread[Differences[-#]<Rest[#]]&]], {n, 30}]
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CROSSREFS
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The case of equality (all adjacent parts having quotient 2) is A154402.
The non-strict version allowing quotients of 2 exactly is A342094.
The version allowing quotients of 2 exactly is A342095.
A000929 counts partitions with no adjacent parts having quotient < 2.
A003114 counts partitions with adjacent parts differing by more than 1.
A034296 counts partitions with adjacent parts differing by at most 1.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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