%I #6 May 22 2021 19:15:58
%S 0,0,0,0,1,0,0,0,0,0,1,1,2,1,1,0,0,0,1,1,2,2,3,3,4,3,3,2,3,2,3,2,3,3,
%T 4,4,5,5,6,6,8,7,8,7,8,7,8,7,8,7,8,7,8,7,9,9,11,11,13,13,15,14,15,14,
%U 15,14,15,14,15,14,16,15,17,16,18,17,19,18,20,19,21,20,22
%N Number of partitions of n into 4 parts such that the largest part is equal to the square of the smallest part.
%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)} [k*(k+1) = n-i-j], where [ ] is the Iverson bracket.
%t Table[Sum[Sum[Sum[KroneckerDelta[k*(k + 1), n - i - j], {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 100}]
%t Table[Count[IntegerPartitions[n,{4}],_?(#[[1]]==#[[-1]]^2&)],{n,0,90}] (* _Harvey P. Dale_, May 22 2021 *)
%K nonn
%O 0,13
%A _Wesley Ivan Hurt_, Jan 06 2021