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Search: id:A101200
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| A101200 |
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Number of partitions of n with rank 3 (the rank of a partition is the largest part minus the number of parts). |
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+0
6
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| 0, 0, 0, 1, 0, 1, 1, 2, 2, 4, 3, 6, 7, 10, 11, 17, 18, 26, 30, 40, 47, 63, 72, 94, 111, 140, 165, 209, 244, 304, 359, 440, 519, 634, 743, 901, 1060, 1273, 1494, 1789, 2092, 2491, 2914, 3449, 4026, 4752, 5530
(list; graph; listen)
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OFFSET
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1,8
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COMMENT
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Column k=3 in the triangle A063995.
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REFERENCES
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George E. Andrews, The Theory of Partitions, Addison-Wesley, Reading, Mass., 1976.
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EXAMPLE
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a(6)=1 because the 11 partitions 6,51,42,411,33,321,3111,222,2211,21111,111111
have ranks 5,3,2,1,1,0,-1,-1,-2,-3,-5, respectively.
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MAPLE
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with(combinat): for n from 1 to 45 do P:=partition(n): c:=0: for j from 1 to nops(P) do if P[j][nops(P[j])]-nops(P[j])=3 then c:=c+1 else c:=c fi od: a[n]:=c: od: seq(a[n], n=1..45);
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CROSSREFS
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Cf. A000041, A063995.
Sequence in context: A090105 A082146 A037145 this_sequence A122585 A057449 A007439
Adjacent sequences: A101197 A101198 A101199 this_sequence A101201 A101202 A101203
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 12 2004
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