This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A339186 #5 Dec 07 2020 01:37:24
%S A339186 0,0,2,1,1,2,2,2,3,2,3,3,3,3,3,3,3,4,5,4,4,4,4,4,4,4,5,5,5,5,5,5,6,5,
%T A339186 5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,8,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,
%U A339186 8,8,8,8,9,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9
%N A339186 Total number of nonzero squares in the partitions of n into 2 parts.
%H A339186 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A339186 a(n) = A339184(n) + A339183(n).
%e A339186 a(8) = 3; The partitions of 8 into two parts are (7,1), (6,2), (5,3) and (4,4). There are 3 total nonzero squares among the parts (namely 1, 4 and 4 ), so a(8) = 3.
%e A339186 a(9) = 2; The partitions of 9 into two parts are (8,1), (7,2), (6,3) and (5,4). Since 1 and 4 are the only nonzero squares among all parts, a(9) = 2.
%t A339186 Table[Sum[Floor[Sqrt[i]] - Floor[Sqrt[i - 1]] + Floor[Sqrt[n - i]] - Floor[Sqrt[n - i - 1]], {i, Floor[n/2]}], {n, 0, 100}]
%Y A339186 Cf. A339183 (number of smaller parts), A339184 (number of larger parts).
%K A339186 nonn,easy
%O A339186 0,3
%A A339186 _Wesley Ivan Hurt_, Nov 26 2020