login
Sum of the odd parts appearing among the third largest parts of the partitions of n into 4 parts.
0

%I #10 Sep 08 2019 10:24:45

%S 0,0,0,0,1,1,2,2,3,3,7,10,17,20,27,30,42,50,67,80,102,115,144,164,200,

%T 227,270,304,363,406,474,526,603,664,761,842,959,1051,1179,1282,1434,

%U 1561,1737,1888,2088,2252,2480,2672,2928,3148,3432,3680,4009,4289

%N Sum of the odd parts appearing among the third largest parts of the partitions of n into 4 parts.

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} j * (j mod 2).

%e Figure 1: The partitions of n into 4 parts for n = 8, 9, ..

%e 1+1+1+9

%e 1+1+2+8

%e 1+1+3+7

%e 1+1+4+6

%e 1+1+1+8 1+1+5+5

%e 1+1+2+7 1+2+2+7

%e 1+1+1+7 1+1+3+6 1+2+3+6

%e 1+1+2+6 1+1+4+5 1+2+4+5

%e 1+1+3+5 1+2+2+6 1+3+3+5

%e 1+1+1+6 1+1+4+4 1+2+3+5 1+3+4+4

%e 1+1+1+5 1+1+2+5 1+2+2+5 1+2+4+4 2+2+2+6

%e 1+1+2+4 1+1+3+4 1+2+3+4 1+3+3+4 2+2+3+5

%e 1+1+3+3 1+2+2+4 1+3+3+3 2+2+2+5 2+2+4+4

%e 1+2+2+3 1+2+3+3 2+2+2+4 2+2+3+4 2+3+3+4

%e 2+2+2+2 2+2+2+3 2+2+3+3 2+3+3+3 3+3+3+3

%e --------------------------------------------------------------------------

%e n | 8 9 10 11 12 ...

%e --------------------------------------------------------------------------

%e a(n) | 3 3 7 10 17 ...

%e --------------------------------------------------------------------------

%e - _Wesley Ivan Hurt_, Sep 08 2019

%t Table[Sum[Sum[Sum[j * Mod[j, 2], {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 50}]

%K nonn

%O 0,7

%A _Wesley Ivan Hurt_, Aug 13 2019