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A130899
Number of partitions of n into "number of partitions of n into 'number of partitions of n into partition numbers' numbers" numbers.
3
1, 2, 3, 4, 6, 9, 11, 15, 19, 25, 31, 41, 49, 61, 75, 91, 109, 134, 156, 188, 221, 262, 305, 361, 416, 485, 560, 648, 740, 858, 972, 1115, 1266, 1441, 1627, 1851, 2078, 2348, 2634, 2965, 3309, 3721, 4138, 4625, 5143, 5728, 6344, 7059, 7792, 8637, 9525, 10529
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 (A130899) is the partition transformation composed with itself four times on the positive integers.
LINKS
EXAMPLE
a(6) = 9 because there are 9 partitions of 6 whose parts are 1,2,3,5,6 which are terms of sequence A130898, which is the number 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@@4)(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, 4]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Oct 26 2015, after Alois P. Heinz *)
CROSSREFS
Cf. A000027, A000041, A007279, A130898, A130900 which are m-fold self-compositions of the "partition transformation" on the counting numbers, for m=0, 1, 2, 4, 5.
Sequence in context: A304428 A132134 A027594 * A007210 A198394 A035947
KEYWORD
nonn
AUTHOR
Graeme McRae, Jun 07 2007
STATUS
approved