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A342096
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Number of integer partitions of n with no adjacent parts having quotient >= 2.
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37
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1, 2, 2, 3, 3, 4, 4, 6, 6, 8, 9, 11, 13, 17, 19, 24, 29, 35, 42, 51, 61, 75, 90, 108, 130, 158, 189, 227, 272, 325, 389, 464, 553, 659, 782, 929, 1102, 1306, 1545, 1824, 2153, 2538, 2989, 3514, 4127, 4842, 5673, 6642, 7766, 9068, 10583, 12335, 14361, 16705
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OFFSET
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1,2
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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(10) = 8 partitions:
1 2 3 4 5 6 7 8 9 A
11 111 22 32 33 43 44 54 55
1111 11111 222 322 53 333 64
111111 1111111 332 432 433
2222 3222 532
11111111 111111111 3322
22222
1111111111
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], 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 version allowing quotients of 2 exactly is A342094.
The strict case 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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