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A309546 Number of even parts in the partitions of n into 5 parts. 0

%I #9 Sep 14 2019 16:50:28

%S 0,0,0,0,0,0,1,2,5,8,15,18,27,34,49,60,81,98,127,150,190,220,271,312,

%T 376,430,511,578,677,760,881,982,1126,1250,1421,1568,1768,1942,2176,

%U 2380,2651,2888,3198,3472,3826,4140,4542,4900,5353,5760,6271,6728,7298

%N Number of even parts in the partitions of n into 5 parts.

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

%F a(n) = Sum_{l=1..floor(n/5)} Sum_{k=l..floor((n-1)/4)} Sum_{j=k..floor((n-k-l)/3)} Sum_{i=j..floor((n-j-k-l)/2)} (((i-1) mod 2) + ((j-1) mod 2) + ((k-1) mod 2) + ((l-1) mod 2) + ((n-i-j-k-l-1) mod 2)).

%e The partitions of n into 5 parts for n = 10, 11, ..

%e 1+1+1+1+10

%e 1+1+1+2+9

%e 1+1+1+3+8

%e 1+1+1+4+7

%e 1+1+1+5+6

%e 1+1+1+1+9 1+1+2+2+8

%e 1+1+1+2+8 1+1+2+3+7

%e 1+1+1+3+7 1+1+2+4+6

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

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

%e 1+1+1+1+8 1+1+2+2+7 1+1+3+4+5

%e 1+1+1+2+7 1+1+2+3+6 1+1+4+4+4

%e 1+1+1+3+6 1+1+2+4+5 1+2+2+2+7

%e 1+1+1+1+7 1+1+1+4+5 1+1+3+3+5 1+2+2+3+6

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

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

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

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

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

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

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

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

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

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

%e n | 10 11 12 13 14 ...

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

%e a(n) | 15 18 27 34 49 ...

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

%e - _Wesley Ivan Hurt_, Sep 12 2019

%t Table[Sum[Sum[Sum[Sum[Mod[i - 1, 2] + Mod[j - 1, 2] + Mod[k - 1, 2] + Mod[l - 1, 2] + Mod[n - i - j - k - l - 1, 2], {i, j, Floor[(n - j - k - l)/2]}], {j, k, Floor[(n - k - l)/3]}], {k, l, Floor[(n - l)/4]}], {l, Floor[n/5]}], {n, 0, 100}]

%K nonn

%O 0,8

%A _Wesley Ivan Hurt_, Aug 07 2019

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)