a(n) is the number of terms in the sum in A075405 (or 0 if no such square exists).

Terms

a(0) =24a(1) =0a(2) =2a(3) =0a(4) =0a(5) =0a(6) =23a(7) =0a(8) =24a(9) =0a(10) =22898a(11) =0a(12) =96a(13) =0a(14) =97a(15) =0a(16) =23a(17) =11a(18) =0a(19) =2a(20) =96a(21) =59a(22) =0a(23) =0a(24) =24a(25) =0a(26) =33a(27) =50a(28) =0a(29) =169