A340732 - OEIS

%I #6 Jan 18 2021 09:56:42

%S 0,0,0,0,1,0,1,0,2,1,2,0,4,0,3,2,5,0,6,0,7,3,5,0,10,3,6,4,10,0,13,0,

%T 11,5,8,6,18,0,9,6,18,0,19,0,16,13,11,0,25,6,19,8,19,0,24,10,26,9,14,

%U 0,38,0,15,19,26,12,31,0,25,11,35,0,45,0,18,23,28,15,37,0,45,19

%N Number of partitions of n into 4 parts such that the product of the smallest and largest parts is equal to the product of the middle two 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*i = k*(n-i-j-k)], where [ ] is the Iverson bracket.

%t Table[Sum[Sum[Sum[KroneckerDelta[j*i, k*(n - i - j - k)], {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 100}]

%o (PARI) for(n=0,70,my(count=0);forpart(p=n,if(#p==4,count+=(p[1]*p[4]==p[2]*p[3])));print1(count,", ")) \\ _Hugo Pfoertner_, Jan 18 2021

%K nonn

%O 0,9

%A _Wesley Ivan Hurt_, Jan 17 2021