A084835 a(n) = A000094(n+4) - A006918(n).

0, 0, 0, 0, 0, 1, 2, 5, 10, 18, 30, 49, 75, 112, 163, 231, 322, 441, 595, 792, 1045, 1361, 1760, 2255, 2871, 3626, 4559, 5691, 7077, 8750, 10780, 13216, 16156, 19662, 23868, 28866, 34828, 41882, 50262, 60138

Offset: 1

Author

Jon Perry, Jul 12 2003

Keywords

• nonn

Comments

Also the number of integer partitions of n - 3 with Durfee square of length > 2, i.e., those with at least 3 parts > 2. The Heinz numbers of these partitions are given by A307515. - Gus Wiseman, Apr 12 2019

Crossrefs

Cf. A000094, A006918, A096771, A115720, A257990, A307515, A325164, A325192.

Programs

Maple

A084845 := proc(n)
    A000094(n+4)-A006918(n)
end proc:
seq(A084845(n),n=1..40) ; # R. J. Mathar, May 17 2016

Mathematica

durf[ptn_]:=Length[Select[Range[Length[ptn]],ptn[[#]]>=#&]];
Table[Length[Select[IntegerPartitions[n],durf[#]>2&]],{n,0,30}] (* Gus Wiseman, Apr 12 2019 *)