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A130898
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Number of partitions of n into "number of partitions of n into partition numbers" numbers.
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3
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1, 2, 3, 5, 6, 10, 12, 18, 22, 30, 37, 50, 59, 78, 93, 118, 140, 176, 206, 255, 297, 362, 421, 507, 585, 699, 803, 949, 1088, 1276, 1455, 1696, 1927, 2230, 2527, 2909, 3284, 3761, 4233, 4825, 5416, 6146, 6879, 7778, 8682, 9778, 10892, 12226, 13582, 15200
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The "partition transformation" of sequence A can be defined as the number of partitions of n into elements of sequence A. This is the partition transformation composed with itself three times on the positive integers.
a(6) = 10 because there are 10 partitions of 6 whose parts are 1,2,3,4,6 which are terms of sequence A007279, which is the number of partitions of n into partition numbers.
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 1..1000
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EXAMPLE
| a(6) = 12 because there are 12 partitions of 6 whose parts are 1,2,3,4,6 which are terms of sequence A007279, which is the number of partitions of n into partition numbers.
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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@@3)(n->n):
seq (a(n), n=1..100); # Alois P. Heinz, Sep 13 2011
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CROSSREFS
| Cf. A000027, A000041, A007279, A130899, 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: A130900 A115029 A023025 * A199016 A088314 A097071
Adjacent sequences: A130895 A130896 A130897 * A130899 A130900 A130901
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KEYWORD
| nonn
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AUTHOR
| Graeme McRae (g_m(AT)mcraefamily.com), Jun 07 2007
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