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A243011
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Sum of the three largest parts in the partitions of 4n into 4 parts.
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0
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3, 34, 159, 489, 1161, 2365, 4336, 7323, 11640, 17646, 25702, 36246, 49761, 66720, 87685, 113263, 144039, 180699, 223974, 274561, 333270, 400956, 478428, 566620, 666511, 779022, 905211, 1046181, 1202965, 1376745, 1568748, 1780119, 2012164, 2266234, 2543586
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OFFSET
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1,1
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LINKS
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Table of n, a(n) for n=1..35.
Index entries for sequences related to partitions
Index entries for linear recurrences with constant coefficients, signature (3,-3,3,-6,6,-3,3,-3,1).
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FORMULA
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a(n) = A238328(n) - A238702(n).
a(n) = A239667(n) + A241084(n) + A242727(n).
a(n) = 4n * A238340(n) - Sum_{i=1..n} A238340(i).
a(n) = (4n-1) * A238702(n) - 4n * A238702(n-1), n > 1.
a(n) = A238328(n) - (1/4) * Sum_{i=1..n} A238328(i)/i.
G.f.: -x*(16*x^6+58*x^5+87*x^4+105*x^3+66*x^2+25*x+3) / ((x-1)^5*(x^2+x+1)^2). - Colin Barker, Sep 22 2014
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EXAMPLE
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Add up the numbers in the first three columns for a(n):
13 + 1 + 1 + 1
12 + 2 + 1 + 1
11 + 3 + 1 + 1
10 + 4 + 1 + 1
9 + 5 + 1 + 1
8 + 6 + 1 + 1
7 + 7 + 1 + 1
11 + 2 + 2 + 1
10 + 3 + 2 + 1
9 + 4 + 2 + 1
8 + 5 + 2 + 1
7 + 6 + 2 + 1
9 + 3 + 3 + 1
8 + 4 + 3 + 1
7 + 5 + 3 + 1
6 + 6 + 3 + 1
7 + 4 + 4 + 1
6 + 5 + 4 + 1
5 + 5 + 5 + 1
9 + 1 + 1 + 1 10 + 2 + 2 + 2
8 + 2 + 1 + 1 9 + 3 + 2 + 2
7 + 3 + 1 + 1 8 + 4 + 2 + 2
6 + 4 + 1 + 1 7 + 5 + 2 + 2
5 + 5 + 1 + 1 6 + 6 + 2 + 2
7 + 2 + 2 + 1 8 + 3 + 3 + 2
6 + 3 + 2 + 1 7 + 4 + 3 + 2
5 + 4 + 2 + 1 6 + 5 + 3 + 2
5 + 3 + 3 + 1 6 + 4 + 4 + 2
4 + 4 + 3 + 1 5 + 5 + 4 + 2
5 + 1 + 1 + 1 6 + 2 + 2 + 2 7 + 3 + 3 + 3
4 + 2 + 1 + 1 5 + 3 + 2 + 2 6 + 4 + 3 + 3
3 + 3 + 1 + 1 4 + 4 + 2 + 2 5 + 5 + 3 + 3
3 + 2 + 2 + 1 4 + 3 + 3 + 2 5 + 4 + 4 + 3
1 + 1 + 1 + 1 2 + 2 + 2 + 2 3 + 3 + 3 + 3 4 + 4 + 4 + 4
4(1) 4(2) 4(3) 4(4) .. 4n
------------------------------------------------------------------------
3 34 159 489 .. a(n)
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MATHEMATICA
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a[1] = 4; a[n_] := (n/(n - 1)) a[n - 1] + 4 n*Sum[(Floor[(4 n - 2 - i)/2] - i) (Floor[(Sign[(Floor[(4 n - 2 - i)/2] - i)] + 2)/2]), {i, 0, 2 n}]; Table[a[n] - Sum[a[i]/i, {i, n}]/4, {n, 30}]
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PROG
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Vec(-x*(16*x^6+58*x^5+87*x^4+105*x^3+66*x^2+25*x+3)/((x-1)^5*(x^2+x+1)^2) + O(x^100)) \\ Colin Barker, Sep 22 2014
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CROSSREFS
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Cf. A238328, A238340, A238702, A239667, A241084.
Sequence in context: A274871 A042041 A180775 * A279130 A266696 A141789
Adjacent sequences: A243008 A243009 A243010 * A243012 A243013 A243014
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KEYWORD
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nonn,easy
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AUTHOR
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Wesley Ivan Hurt, May 28 2014
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STATUS
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approved
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