T(n,k)=Number of (n+1)X(n+1) -k..k symmetric matrices with every 2X2 subblock having sum zero.

Terms

a(0) =5a(1) =13a(2) =9a(3) =25a(4) =35a(5) =17a(6) =41a(7) =91a(8) =97a(9) =33a(10) =61a(11) =189a(12) =337a(13) =275a(14) =65a(15) =85a(16) =341a(17) =881a(18) =1267a(19) =793a(20) =129a(21) =113a(22) =559a(23) =1921a(24) =4149a(25) =4825a(26) =2315a(27) =257a(28) =145a(29) =855