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A073119
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Total number of parts which are powers of 2 in all partitions of n.
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1
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0, 1, 1, 4, 5, 10, 14, 26, 35, 56, 77, 116, 157, 226, 302, 424, 560, 762, 998, 1334, 1727, 2270, 2914, 3779, 4809, 6163, 7781, 9875, 12378, 15565, 19383, 24191, 29934, 37093, 45643, 56201, 68789, 84212, 102564, 124903, 151424, 183499, 221508
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 1..2000
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FORMULA
| a(n) = Sum_{k=1..n} A007814(k)*A000041(n-k).
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MAPLE
| p2:= proc(n) p2(n):= is(n=2^ilog2(n)) end: p2(1):= false:
b:= proc(n, i) option remember; local t, l;
if n<0 then [0, 0]
elif n=0 then [1, 0]
elif i<1 then [0, 0]
else t:= b(n, i-1);
l:= b(n-i, i);
[t[1]+l[1], t[2]+l[2]+ `if` (p2(i), l[1], 0)]
fi
end:
a:= n-> b(n, n)[2]:
seq (a(n), n=1..50); # Alois P. Heinz, Sep 29 2011
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MATHEMATICA
| Needs["DiscreteMath`Combinatorica`"]; f[n_] := Length[ Select[ Log[2, Flatten[ Partitions[n]]], IntegerQ[ # ] && # > 0 & ]]; Table[ f[n], {n, 1, 45}]
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CROSSREFS
| Cf. A024786, A000070.
Sequence in context: A094415 A114517 A116930 * A002257 A101528 A119040
Adjacent sequences: A073116 A073117 A073118 * A073120 A073121 A073122
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KEYWORD
| easy,nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 24 2002
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EXTENSIONS
| Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 26 2002
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