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A222048
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Sum of largest parts of all partitions of n into an even number of parts.
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8
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0, 0, 1, 2, 6, 9, 18, 26, 45, 62, 99, 135, 204, 274, 396, 527, 741, 973, 1333, 1736, 2331, 3007, 3970, 5079, 6615, 8393, 10796, 13605, 17320, 21673, 27339, 34001, 42540, 52597, 65324, 80332, 99127, 121274, 148745, 181131, 220956, 267852, 325114, 392476, 474178
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OFFSET
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0,4
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COMMENTS
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A222047(n) + a(n) = A006128(n).
A222047(n) - a(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) = 18: partitions of 6 into an even number of parts are [1,1,1,1,1,1], [2,2,1,1], [3,1,1,1], [3,3], [4,2], [5,1], sum of largest parts is 1+2+3+3+4+5 = 18.
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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)[2]:
seq(a(n), n=0..50);
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MATHEMATICA
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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][[2]]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Feb 02 2017, translated from Maple *)
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CROSSREFS
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Cf. A006128, A211373, A222044, A222045, A222046, A222047, A222049.
Sequence in context: A156222 A002886 A028724 * A156190 A285446 A076738
Adjacent sequences: A222045 A222046 A222047 * A222049 A222050 A222051
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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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