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A342095
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Number of strict integer partitions of n with no adjacent parts having quotient > 2.
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35
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1, 1, 2, 1, 2, 3, 3, 2, 4, 4, 6, 7, 6, 8, 10, 9, 13, 16, 17, 20, 25, 26, 29, 36, 40, 45, 55, 61, 69, 81, 90, 103, 119, 132, 154, 176, 196, 225, 254, 282, 323, 364, 403, 458, 519, 582, 655, 735, 822, 922, 1035, 1153, 1290, 1441, 1600, 1788, 1997, 2217, 2468
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OFFSET
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1,3
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COMMENTS
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The decapitation of such a partition (delete the greatest part) is term-wise greater than or equal to its negated first-differences.
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LINKS
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EXAMPLE
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The a(1) = 1 through a(15) = 10 partitions (A..F = 10..15):
1 2 3 4 5 6 7 8 9 A B C D E F
21 32 42 43 53 54 64 65 75 76 86 87
321 421 63 532 74 84 85 95 96
432 4321 542 543 643 653 A5
632 642 742 743 654
5321 5421 6421 842 753
6321 5432 843
7421 6432
8421
54321
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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 reciprocal version (no adjacent parts having quotient < 2) is A000929.
The case of equality (all adjacent parts having quotient 2) is A154402.
The non-strict version without quotients of 2 exactly is A342096.
The version without quotients of 2 exactly is A342097.
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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