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A239186
Sum of the largest two parts in the partitions of 4n into 4 parts with smallest part equal to 1.
4
2, 23, 93, 243, 492, 878, 1432, 2165, 3123, 4337, 5810, 7596, 9726, 12195, 15065, 18367, 22088, 26298, 31028, 36257, 42063, 48477, 55470, 63128, 71482, 80495, 90261, 100811, 112100, 124230, 137232, 151053, 165803, 181513, 198122, 215748, 234422, 254075
OFFSET
1,1
FORMULA
G.f.: x*(10*x^6+39*x^5+61*x^4+76*x^3+49*x^2+19*x+2) / ((x-1)^4*(x^2+x+1)^2). - Colin Barker, Mar 12 2014
a(n) = 2*a(n-1)-a(n-2)+2*a(n-3)-4*a(n-4)+2*a(n-5)-a(n-6)+2*a(n-7)-a(n-8). - Wesley Ivan Hurt, Nov 19 2021
EXAMPLE
For a(n) add the numbers in the first two columns.
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 + 1 + 1 + 1 9 + 4 + 2 + 1
8 + 2 + 1 + 1 8 + 5 + 2 + 1
7 + 3 + 1 + 1 7 + 6 + 2 + 1
6 + 4 + 1 + 1 9 + 3 + 3 + 1
5 + 5 + 1 + 1 8 + 4 + 3 + 1
7 + 2 + 2 + 1 7 + 5 + 3 + 1
5 + 1 + 1 + 1 6 + 3 + 2 + 1 6 + 6 + 3 + 1
4 + 2 + 1 + 1 5 + 4 + 2 + 1 7 + 4 + 4 + 1
3 + 3 + 1 + 1 5 + 3 + 3 + 1 6 + 5 + 4 + 1
1 + 1 + 1 + 1 3 + 2 + 2 + 1 4 + 4 + 3 + 1 5 + 5 + 5 + 1
4(1) 4(2) 4(3) 4(4) .. 4n
------------------------------------------------------------------------
2 23 93 243 .. a(n)
MATHEMATICA
b[n_] := Sum[((4 n - 2 - i)*Floor[(4 n - 2 - i)/2] - i (4 n - 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*(10*x^6+39*x^5+61*x^4+76*x^3+49*x^2+19*x+2)/((x-1)^4*(x^2+x+1)^2) + O(x^100)) \\ Colin Barker, Sep 22 2014
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Mar 11 2014
STATUS
approved