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 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.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000
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.
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
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, 3]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Oct 26 2015, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Graeme McRae, Jun 07 2007
STATUS
approved