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A222047
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Sum of largest parts of all partitions of n into an odd number of parts.
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8
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0, 1, 2, 4, 6, 11, 17, 28, 41, 66, 93, 140, 195, 282, 384, 541, 722, 992, 1311, 1762, 2299, 3045, 3929, 5127, 6559, 8458, 10726, 13689, 17225, 21780, 27224, 34134, 42387, 52769, 65138, 80544, 98887, 121538, 148456, 181456, 220590, 268252, 324677, 392961
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OFFSET
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0,3
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COMMENTS
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a(n) + A222048(n) = A006128(n).
a(n) - A222048(n) = A222049(n).
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..1000
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EXAMPLE
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a(6) = 17: partitions of 6 into an odd number of parts are [2,1,1,1,1], [2,2,2], [3,2,1], [4,1,1], [6], sum of largest parts is 2+2+3+4+6 = 17.
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MAPLE
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b:= proc(n, i) option remember; [`if`(n=i, n, 0), 0]+
`if`(i>n, [0, 0], b(n, i+1)+(l-> [l[2], l[1]])(b(n-i, i)))
end:
a:= n-> b(n, 1)[1]:
seq(a(n), n=0..50);
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MATHEMATICA
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Table[Total[Max[#]&/@Select[IntegerPartitions[n], OddQ[Length[#]]&]], {n, 0, 50}] (* Harvey P. Dale, Apr 19 2014 *)
b[n_, i_] := b[n, i] = {If[n==i, n, 0], 0} + If[i>n, {0, 0}, b[n, i+1] + Reverse[b[n-i, i]]]; a[n_] := b[n, 1][[1]]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Aug 30 2016, after Alois P. Heinz *)
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CROSSREFS
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Cf. A006128, A211373, A222044, A222045, A222046, A222048, A222049.
Sequence in context: A336307 A336134 A255214 * A210520 A018144 A115315
Adjacent sequences: A222044 A222045 A222046 * A222048 A222049 A222050
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Feb 06 2013
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STATUS
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approved
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