A238640 Position of [n, n, ..., n] (n n's) in Mathematica-ordered list of partitions of n^2.

1, 1, 3, 19, 168, 1582, 15546, 157051, 1625368, 17159223, 184277224, 2008388660, 22172275440, 247558926150, 2791793968821, 31764451979736, 364283594455091, 4207485803818522, 48908343969469479, 571811846280602486, 6720473048598172508, 79363083519870386700

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..140

Example

The partitions of 4 in Mathematica order are 4, 31, 22, 211, 1111.  The position of 22 is a(2) = 3.

Maple

b:= proc(n, i) option remember; `if`(n=0, 1,
      `if`(i<1, 0, b(n, i-1) +`if`(i>n, 0, b(n-i, i))))
    end:
a:= n-> 1 +add(b(n^2-j, j), j=n+1..n^2):
seq(a(n), n=0..20);  # Alois P. Heinz, Sep 03 2014

Mathematica

r[n_] := Table[n, {k, 1, n}]; Flatten[Table[Position[IntegerPartitions[n^2], r[n]], {n, 0, 8}]]
b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, b[n, i-1]+If[i>n, 0, b[n-i, i]]]]; a[n_] := 1+Sum[b[n^2-j, j], {j, n+1, n^2}]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Oct 28 2015, after Alois P. Heinz *)

Crossrefs

Cf. A000290, A072213, A080577 (Mathematica ordering), A238638, A238639, A330661, A332706.

Sequence in context: A201123 A260700 A105624 * A349253 A080835 A080836

Adjacent sequences: A238637 A238638 A238639 * A238641 A238642 A238643

Keyword

nonn

Author

Clark Kimberling, Mar 04 2014

Extensions

a(9)-a(21) from Alois P. Heinz, Sep 03 2014

Status

approved