A239186 Sum of the largest two parts in the partitions of 4n into 4 parts with smallest part equal to 1.
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
Examples
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
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2 23 93 243 .. a(n)
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- Index entries for sequences related to partitions
- Index entries for linear recurrences with constant coefficients, signature (2,-1,2,-4,2,-1,2,-1).
Programs
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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}] -
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
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