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A350844
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Number of strict integer partitions of n with no difference -2.
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16
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1, 1, 1, 2, 1, 3, 3, 4, 4, 7, 7, 8, 11, 12, 15, 18, 21, 23, 31, 32, 40, 45, 54, 59, 73, 78, 94, 106, 122, 136, 161, 177, 203, 231, 259, 293, 334, 372, 417, 476, 525, 592, 663, 742, 821, 931, 1020, 1147, 1271, 1416, 1558, 1752, 1916, 2137, 2357, 2613, 2867
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OFFSET
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0,4
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LINKS
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EXAMPLE
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The a(1) = 1 through a(12) = 11 partitions (A..C = 10..12):
1 2 3 4 5 6 7 8 9 A B C
21 32 51 43 62 54 73 65 84
41 321 52 71 63 82 74 93
61 521 72 91 83 A2
81 541 92 B1
432 721 A1 543
621 4321 632 651
821 732
741
921
6321
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], FreeQ[Differences[#], 0|-2]&]], {n, 0, 30}]
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CROSSREFS
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The version for no difference 0 is A000009.
The version for subsets of prescribed maximum is A005314.
A027187 counts partitions of even length.
Cf. A000929, A003000, A018819, A040039, A045690, A045691, A154402, A303362, A323094, A342095, A342097.
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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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