A101200 Number of partitions of n with rank 3 (the rank of a partition is the largest part minus the number of parts).

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

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

Seiichi Manyama, Table of n, a(n) for n = 1..1000

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, A101198, A101199.

Sequence in context: A238787 A293170 A341469 * A122585 A057449 A308601

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