A238639 Position of [n, n-1, ..., 2, 1] in Mathematica-ordered list of partitions of n(n+1)/2.

1, 1, 2, 6, 23, 103, 498, 2493, 12741, 66224, 348963, 1859009, 9994196, 54155387, 295477841, 1621962199, 8951635343, 49644856801, 276540258555, 1546630084062, 8681889729354, 48900895532763, 276302483274825, 1565747892473958, 8896975706929141, 50683901455201860

Offset: 0

Author

Clark Kimberling, Mar 04 2014

Keywords

• nonn

Examples

			The partitions of 6 in Mathematica order are 6, 51, 42, 411, 33, 321, 3111, 222, 2211, 21111, 111111.  The position of 321 is a(3) = 6.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200
• Manfred Scheucher, C Code

Crossrefs

Cf. A000217, A080577 (Mathematica ordering), A238638, A238640, A330661, A332706.

Programs

Maple

g:= (n, i)-> `if`(n=0, 1, g(n-i+1, i-1)+ b(n-i, i)):
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-> (m-> add(b(m-j, min(j, m-j)), j=n+1..m)+
                 g(m-n, n))(n*(n+1)/2):
seq(a(n), n=0..25);  # Alois P. Heinz, Jun 03 2015

Mathematica

r[n_] := Table[n - k, {k, 0, n - 1}]; Flatten[Table[Position[IntegerPartitions[n (n + 1)/2], r[n]], {n, 0, 2}]]
g[n_, i_] := If[n==0, 1, g[n-i+1, i-1] + b[n-i, i]]; 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_] := Function[m, Sum[b[m-j, Min[j, m-j]], {j, n+1, m}] + g[m-n, n]][n(n+1)/2]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Oct 28 2015, after Alois P. Heinz *)

Extensions

a(13)-a(17) from Manfred Scheucher, Jun 01 2015

a(18)-a(25) from Alois P. Heinz, Jun 02 2015