A101200 - OEIS

%I #12 Jan 24 2022 09:01:44

%S 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,

%T 165,209,244,304,359,440,519,634,743,901,1060,1273,1494,1789,2092,

%U 2491,2914,3449,4026,4752,5530,6502,7561,8852,10272,11997,13889,16171,18695,21700,25041,29002

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

%C Column k=3 in the triangle A063995.

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

%H Seiichi Manyama, <a href="/A101200/b101200.txt">Table of n, a(n) for n = 1..1000</a>

%e 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.

%p 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);

%Y Cf. A000041, A063995, A101198, A101199.

%K nonn

%O 1,8

%A _Emeric Deutsch_, Dec 12 2004

%E More terms, _Joerg Arndt_, Oct 07 2012