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A101200 Number of partitions of n with rank 3 (the rank of a partition is the largest part minus the number of parts). 5
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, 6502, 7561, 8852, 10272, 11997, 13889, 16171, 18695, 21700, 25041, 29002 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

Column k=3 in the triangle A063995.

REFERENCES

George E. Andrews, The Theory of Partitions, Addison-Wesley, Reading, Mass., 1976.

LINKS

Table of n, a(n) for n=1..58.

EXAMPLE

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.

MAPLE

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);

CROSSREFS

Cf. A000041, A063995.

Sequence in context: A238790 A238787 A293170 * A122585 A057449 A286931

Adjacent sequences:  A101197 A101198 A101199 * A101201 A101202 A101203

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Dec 12 2004

EXTENSIONS

More terms, Joerg Arndt, Oct 07 2012

STATUS

approved

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Last modified April 23 03:26 EDT 2019. Contains 322380 sequences. (Running on oeis4.)