A091356 Number of planar partitions of n with exactly 2 rows.

1, 2, 5, 9, 18, 30, 53, 85, 139, 215, 336, 504, 760, 1115, 1635, 2351, 3375, 4770, 6725, 9368, 13006, 17885, 24510, 33319, 45139, 60743, 81457, 108610, 144334, 190844, 251542, 330082, 431825, 562710, 731154, 946644, 1222305, 1573155, 2019471

Offset: 2

Author

Christian G. Bower, Jan 02 2004

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..10000

Crossrefs

Column 2 of A091355.

Cf. A000219, A091357, A091358, A091359, A091360.

Programs

Maple

b:= proc(n, k) option remember; `if`(n=0, 1, add(add(min(d, k)
     *d, d=numtheory[divisors](j))*b(n-j, k), j=1..n)/n)
    end:
a:= n-> b(n, 2)-b(n, 1):
seq(a(n), n=2..50);  # Alois P. Heinz, Oct 02 2018

Mathematica

b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[Sum[Min[d, k] d, {d, Divisors[j]}] b[n - j, k], {j, 1, n}]/n];
a[n_] :=  b[n, 2] - b[n, 1];
a /@ Range[2, 50] (* Jean-François Alcover, Oct 28 2020, after Alois P. Heinz *)

Formula

a(n) = A000990(n) - A000041(n).