A130900 Number of partitions of n into {number of partitions of n into "number of partitions of n into 'number of partitions of n into partition numbers' numbers" numbers} numbers.

1, 2, 3, 5, 6, 10, 12, 17, 22, 29, 36, 48, 58, 73, 91, 111, 134, 165, 197, 236, 283, 335, 395, 468, 547, 639, 747, 866, 1001, 1160, 1334, 1530, 1757, 2007, 2286, 2606, 2958, 3349, 3793, 4281, 4821, 5430, 6097, 6833, 7657, 8559, 9549, 10652, 11858, 13178

Offset

1,2

Comments

The "partition transformation" of sequence A can be defined as the number of partitions of n into elements of sequence A. This sequence (A130900) is the partition transformation composed with itself five times on the positive integers.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Example

a(6) = 10 because there are 10 partitions of 6 whose parts are 1,2,3,4,6 which are terms of sequence A130899, which is the number of partitions of n into numbers of partitions of n into numbers of partitions of n into partition numbers.

Maple

pp:= proc(p) local b;
       b:= proc(n, i)
             if n<0 then 0
           elif n=0 then 1
           elif i<1 then 0
           else b(n, i):= b(n, i-1) +b(n-p(i), i)
             fi
           end;
       n-> b(n, n)
     end:
a:= (pp@@5)(n->n):
seq(a(n), n=1..100);  # Alois P. Heinz, Sep 13 2011

Mathematica

pp[p_] := Module[{b}, b[n_, i_] := Which[n < 0, 0, n == 0, 1, i < 1, 0, True, b[n, i] = b[n, i - 1] + b[n - p[i], i]]; b[#, #]&]; a = Nest[pp, Identity, 5]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Oct 26 2015, after Alois P. Heinz *)

Crossrefs

Cf. A000027, A000041, A007279, A130898, A130899, A130900 which are m-fold self-compositions of the "partition transformation" on the counting numbers, m=0, 1, 2, 4, 5.

Sequence in context: A213212 A341124 A008627 * A007211 A027593 A115029

Adjacent sequences: A130897 A130898 A130899 * A130901 A130902 A130903

Keyword

nonn

Author

Graeme McRae, Jun 07 2007

Status

approved