T(n,k)=Number of strings of n numbers x(i) in -k..k with sums of x(i) and of x(i)*x(i+1) both zero.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =3a(6) =1a(7) =1a(8) =5a(9) =7a(10) =1a(11) =1a(12) =7a(13) =15a(14) =21a(15) =1a(16) =1a(17) =9a(18) =21a(19) =81a(20) =45a(21) =1a(22) =1a(23) =11a(24) =33a(25) =169a(26) =237a(27) =121a(28) =1a(29) =1