|
| |
|
|
A239059
|
|
Sum of the two smallest parts from the partitions of 4n into 4 parts with smallest part = 1.
|
|
7
|
|
|
|
2, 9, 27, 61, 108, 178, 276, 395, 549, 743, 966, 1236, 1558, 1917, 2335, 2817, 3344, 3942, 4616, 5343, 6153, 7051, 8010, 9064, 10218, 11441, 12771, 14213, 15732, 17370, 19132, 20979, 22957, 25071, 27278, 29628, 32126, 34725, 37479, 40393, 43416, 46606, 49968
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
LINKS
|
|
|
|
FORMULA
|
G.f.: -x*(x^2+x+2)*(2*x^4-3*x^3-4*x^2-2*x-1) / ((x-1)^4*(x^2+x+1)^2). - Colin Barker, Mar 10 2014
|
|
|
EXAMPLE
|
For a(n) add the smallest two parts in the partitions with smallest part equal to 1..
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
------------------------------------------------------------------------
2 9 27 61 .. a(n)
|
|
|
MATHEMATICA
|
b[n_] := Sum[((i + 2) (Floor[(4 n - 2 - i)/2] - i)) (Floor[(Sign[(Floor[(4 n - 2 - i)/2] - i)] + 2)/2]), {i, 0, 2 n}]; Table[b[n], {n, 50}]
|
|
|
PROG
|
(PARI) Vec(-x*(x^2+x+2)*(2*x^4-3*x^3-4*x^2-2*x-1)/((x-1)^4*(x^2+x+1)^2) + O(x^100)) \\ Colin Barker, Sep 22 2014
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
