A216669 Total number of parts in all partitions of n into 2 sizes of parts (A002133).

2, 5, 14, 20, 39, 52, 74, 102, 134, 158, 208, 259, 284, 361, 409, 488, 538, 634, 678, 838, 857, 1006, 1038, 1270, 1264, 1495, 1500, 1776, 1761, 2084, 2062, 2443, 2300, 2795, 2680, 3194, 3076, 3544, 3403, 4080, 3804, 4518, 4282, 5037, 4673, 5626, 5127, 6088

Offset: 3

Author

Geoffrey Critzer, Sep 13 2012

Keywords

• nonn

Comments

Also column k=2 of A255768. - Omar E. Pol, Jul 26 2015

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..1000

Crossrefs

Cf. A002133, A216665, A255768.

Programs

Mathematica

nn=40;ss=Sum[Sum[y^2 x^(i+j)/(1-y x^i)/(1-y x^j),{j,1,i-1}], {i,1,nn}]; CoefficientList[Series[D[ss,y]/.y->1,{x,0,nn}],x]

Formula

a(n) = Sum_{k=2..n-1} k * A216665(n,k).