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Search: id:A101199
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| A101199 |
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Number of partitions of n with rank 2 (the rank of a partition is the largest part minus the number of parts). |
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+0
2
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| 0, 0, 1, 0, 1, 1, 2, 2, 3, 3, 6, 6, 9, 10, 15, 16, 23, 27, 36, 42, 55, 64, 84, 98, 124, 147, 185, 217, 270, 318, 391, 461, 562, 661, 802, 942, 1132, 1331, 1592, 1864, 2220, 2597, 3077, 3593, 4240
(list; graph; listen)
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OFFSET
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1,7
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COMMENT
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Column k=2 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])=2 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: A038716 A035642 A133392 this_sequence A032155 A116932 A116450
Adjacent sequences: A101196 A101197 A101198 this_sequence A101200 A101201 A101202
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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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